ultrafast electron crystallography studies ......presents a unique system to study the interplay...
TRANSCRIPT
ULTRAFAST ELECTRON CRYSTALLOGRAPHY STUDIES OF CHARGE-DENSITY WAVES
MATERIALS AND NANOSCALE ICE
By
Tzong-Ru Terry Han
A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics - Doctor of Philosophy
2015
ABSTRACT
ULTRAFAST ELECTRON CRYSTALLOGRAPHY STUDIES OF CHARGE-DENSITY WAVES
MATERALS AND NANOSCALE ICE
By
Tzong-Ru Terry Han
The main focus of this dissertation is centered around the study of structural dynamics and phase
transition in charge-density wave (CDW) materials. Due to their quasi-reduced dimensionality, a CDW
presents a unique system to study the interplay between electron and lattice, effect of symmetry breaking,
and electronic condensates. Femtosecond time-resolved pump-probe technique with electron
crystallography offers the perfect tool to disentangle the two main players in CDW: electrons and ions.
By illumination with intense femtosecond optical pulses to increase the electron energy, we monitor how
the energy flows to other subsystems, and explore regions of the energy landscape that are not accessible
through conventional methods.
Taking advantages of the uniaxial CDW formation of CeTe3 that allows us to differentiate non-
CDW-related contributions to the lattice response, we isolate the CDW-related structural response from
the thermal effects on lattice. From the two-component structural dynamics, we examine how strongly
the electron and lattice couple to each other, and further distinguish the internal energy transfer between
each charge and lattice subsystems. From this CeTe3 experiment, we provide an explanation to a
signature phenomenon belonging to "classical Peierls" CDW systems.
Compared to the classical CDW in CeTe3, 1T-TaS2 is at the other end of spectrum with its well
decorated phase diagram including almost all flavors of CDW, Mott insulating, and superconducting
states. Utilizing femtosecond photo-doping, we explore the energy landscape for states or phases that are
not accessible by other conventional means, like chemical doping and pressure induced modification.
The remaining part of this dissertation presents the journey we embarked on when trying to
unveil the mystery of water, the ubiquitous molecule that sustains life on earth. Utilizing water delivery
system designed specifically for our ultra-high-vacuum chamber, we explore the structural change near
the water phase boundary and carrier redistribution or diffusion at the water/nanoparticle/silicon interface.
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To my family
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ACKNOWLEDGMENTS
First and foremost, I would like to thank my advisor Prof. Chong-Yu Ruan for his patience,
support, advice, and guidance. I came to MSU wishing to learn "how to do science" but earned more than
that. He taught me how to manage every project in life with planning, perspective, and the desire to
overachieve.
Next, I would like to thank my comrades, Zhensheng Tao and Kiseok Chang. Either in the lab or
outside school, they helped me solve the problems I countered, shared the up-and-down moments and
emotions with me, and carried me on their shoulder along the way. I also want to thank Faran Zhou for
his help and company on many projects, especially when I was not available in the lab.
I acknowledge my colleagues and collaborators for their advice and support throughout my time
at MSU. Thank to Dr. Christos D. Malliakas and Prof. Kanatzidis at Northwestern University for their
high-quality samples and scientific support for the CDW projects reported in this dissertation. Thanks to
Prof. John McGuire for his guidance in the nonlinear optics setup for our water experiment. Thanks to
Prof. William Pratt for his guidance when I T.A.ed his class in 2008. Thanks to Fei Yuan for his
theoretical computation and helping hands in the lab. Thanks to two excellent MSU undergraduate
students, Peter Lee and Thiago Szymanski, for their support and assistance in almost every project
described in my dissertation. Thanks to every REU student I worked with who helped us advance many
projects during the summer.
Dr. Reza Loloee helped me greatly with his knowledge of many instruments and facilities that
were crucial to my projects. Dr. Xudong Fan at the Center for Advanced Microscopy helped me on many
problems I encountered with sample preparation and characterization. Dr. Baokang Bi trained and
advised me to utilize the equipments in the cleanroom and pushed the results I could obtain to the limit
with those state-of-the-art instruments. To the machine shop staff Tom Palazzolo, Tom Hudson, Jum
Muss, and Rob Bennett for their impeccable skills in producing precise instruments for my projects and
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their patience on teaching me how to keep all my fingers when I was working in the student machine shop.
Big thanks are also due to Cathy Cords, Debbie Barratt, and Kim Crosslan for their fantastic
administrative support. In all, I would like to thank everyone in the physics department at MSU for their
friendly smiles and nurturing conversations. The MSU family is warmer than the freezing Michigan
weather.
On the personal side, I would like to thank the unconditional love from my parents. Last but not
least, I want to thank my wife Peggy Wu. She gave me the freedom to pursue my career goal and the
courage to keep going when I wanted to give up.
I came to MSU seeking knowledge and advice, but I earned life-changing experience, life-long
friendship, and unforgettable memories.
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TABLE OF CONTENTS
LIST OF TABLES......................................................................................................................................ix
LIST OF FIGURES...................................................................................................................................x
CHAPTER 1..................................................................................................................................................1
Strongly Correlated Complex Materials........................................................................................................1
1.1 Colossal Magnetoresistance Magnanites............................................................................2
1.2 Cuprate Superconductor.......................................................................................................6
1.3 Experimental Challenges.....................................................................................................9
CHAPTER 2................................................................................................................................................10
Charge-Density Waves Materials................................................................................................................10
2.1 Overview on Charge-Density Waves.................................................................................11
2.1.1 Nearly Free Electron in One Dimensional Conduction Band...............................11
2.1.2 The Lindhard Response Function of Electron Gas...............................................13
2.1.3 Instabilities in a One-Dimensional Electron Gas..................................................18
2.1.4 The Kohn Anomaly and the Peierls Transition....................................................20
2.1.5 Collective Excitation of Charge-Density Waves..................................................27
2.2 Charge-Density Waves Investigated by Various Techniques and Scientific Outstanding
Questions............................................................................................................................29
CHAPTER 3................................................................................................................................................32
Ultrafast Electron Crystallography Techniques for Studying Low Dimensional Material CeTe3...............32
3.1 Diffraction Theory.............................................................................................................33
3.1.1 Diffraction Condition............................................................................................33
3.1.2 Scattered Intensity.................................................................................................35
3.1.3 The Debye Waller Effect......................................................................................39
3.2 CeTe3 Sample Preparation and Characterization...............................................................42
3.3 Experimental Setup............................................................................................................47
CHAPTER 4................................................................................................................................................50
Structural Dynamics of Charge-Density Waves..........................................................................................50
4.1 Background on CeTe3........................................................................................................51
4.2 Experiments on CeTe3.......................................................................................................55
4.2.1 CeTe3 Experimental Setup and Methods..............................................................55
4.2.2 Asymmetric Characters of CeTe3.........................................................................57
4.2.3 Dynamics of Order Parameter of CDW in CeTe3.................................................59
4.2.4 Cooperativity Between Electronic and Structural Subsystems.............................62
4.2.5 Summary...............................................................................................................65
CHAPTER 5................................................................................................................................................67
Phase Transition of Charge-Density Waves................................................................................................67
5.1 Crystal Structure and Charge-Density Waves of 1T-TaS2................................................68
5.2 Exploration of Meta-Stability and Hidden Phases of 1T-TaS2.........................................71
5.3 Additional Materials for 1T-TaS2 experiment...................................................................85
5.3.1 Sample Preparation...............................................................................................85
5.3.2 Experimental Details.............................................................................................87
5.3.3 Data Analysis for 1T-TaS2 Experiment...............................................................88
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5.3.4 Calculation of Energy and Photon Density..........................................................89
5.3.5 Constructing Phase Diagram................................................................................91
CHAPTER 6................................................................................................................................................92
Dynamics of Nanoscale Water on Surface..................................................................................................92
6.1 Structure and Dynamics of Water......................................................................................93
6.2 Experiment Setup...............................................................................................................97
6.3 Generation of Mid-IR Excitation Laser via Nonlinear Optics.........................................100
6.4 Ice/Water Deposition on Substrate Using Molecular Beam Doser.................................107
6.5 Ice/Water Experiment Result...........................................................................................112
CHAPTER 7..............................................................................................................................................115
Surface-Plasmonic-Resonance Enhanced Interfacial Charge Transfer.....................................................115
7.1 Introduction......................................................................................................................116
7.2 Ultrafast Diffractive Photovoltammetry Methodology and Experiment Setup...............118
7.3 Charge Transfer between Nanoparticles and Substrate Enhanced by Surface Plasmon
Resonance Excitation with the Coverage of Water-Ice...................................................120
CHAPTER 8..............................................................................................................................................125
Summary....................................................................................................................................................125
APPENDICES...........................................................................................................................................127
Appendix A Electron Counting and Statistical Uncertainties.................................................128
Appendix B Two Component Fitting and Statistical Analysis...............................................130
Appendix C Carbon Nanotube Sample Preparation................................................................133
Appendix D Tsunami Alignment............................................................................................135
Appendix E Optimization at Spitfire for Optimal Output of Mid-IR Laser...........................138
Appendix F Gold Nano-Particle Deposition on ITO..............................................................139
BIBLIGRAPHY………………………………………………………………………………………….140
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LIST OF TABLES
Table 2.1.1 Various broken-symmetry ground states of one-dimensional metals [Dre 2002]……….19
Table 5.1.1 The different CDW phase in 1T-TaS2 and their manifestation in reciprocal space. The
values of transition temperature and angle associated with different CDW phases under
the thermodynamic conditions (cooling and warming) are taken from [Spi 1997] [Ish
1991]..................................................................................................................…...70
x
LIST OF FIGURES
Figure 1.1.1 Previous studies on CMR. (a) Magnetoresistance measurement at room temperature for
La-Ba-Mn-O thin films. (b) Temperature dependence of resistivity (R), resistivity (),
and magnetization (M) of La-Ca-Mn-O films.....................................................................3
Figure 1.1.2 Previous studies on CMR. (a) Induced change in transmitted electric field. (b) Induced
change in real conductivity..................................................................................................4
Figure 1.1.3 Previous studies on CMR. (a) Contribution of spin and phonon to conductivity at
different temperature (b) Phase diagram of La1-xCaxMnO3 showing phases including
charge-ordering (CO), antiferromagnet (AF), canted antiferromagnet (CAF),
ferromagnetic (FM), and ferromagnetic insulator (FI). (c) Linescan of TEM images in the
a (red line) and c (blue line) showing the satellite peaks only present in the a direction.
(d) and (e) Differential resistivity versus d.c. bias applied in the a (red lines) and c (blue
lines) directions at various temperatures..............................................................................5
Figure 1.2.1 Previous studies on Cuprates. (a) Diffraction intensity crossing a common point at
different delay time at different fluence. (b) Threshold in fluence that would initiate the
phase transition. (c) Typical photoemission data at Fermi surface showing change in
electron dispersion and spectra after optical excitation. (d) Dynamics of superconducting
gap magnitude at two locations.........................................................................................7
Figure 2.1.1 Band structure of two electron models. (a) Energy versus wavevector for a free
electron (b) Energy versus wavevector, or band structure, for an electron in a monatomic
linear lattice of lattice constant [Kit 2004].....................................................................12
Figure 2.1.2 Responses with different dimensions. (a) The Lindhard response function for different
dimensions. (b) and (c) The Fermi surface, noted in red lines, and Fermi nesting, the
condition with a common paring wavevector at Fermi surface. (d) The pairs of one full
and one empty states can be connected by the wavevector ................................15
Figure 2.1.3 Low-dimension gas. (a) Fermi surface of a quasi-one-dimensional electron gas [Grü
1994]. (b) The response function of one-dimensional electron gas at various temperatures
[Hee 1979].........................................................................................................................17
Figure 2.1.4 The Kohn anomaly. (a) The Kohn anomaly of acoustic phonon frequency showing Kohn
anomaly at temperature above the mean field transition temperature. (b) Phonon
dispersion relationship of 1D, 2D, and 3D dimensional metals [Grü 1994].......22
Figure 2.1.5 The single particle band, electron density, and lattice distortion in (a) state above
and (b) in CDW state at . (c) The temperature dependence of band gap and
the renormalized phonon frequency . Both carries a characteristic dependence of
.....................................................................................................................25
Figure 2.1.6 CDW states. (a) CDW ground state (b) Phase mode (c) Amplitude mode. The dotted
lines represents the electronic part of charge-density wave while the arrow indicates the
displacement of ion core, as red dots, from the equilibrium position...............................27
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Figure 2.2.1 Previous studies on 1T-TaS2. (a) The time evolution of normalized reflectivity measured
at different sample temperature, T = 45 and 110 K displayed in log scale to highlight the
two time scale in relaxation [Dem 1999]. (b) the temperature dependence of relaxation
time of 1T-TaS2, plotted with result taken upon warming in open symbols and cooling in
solid symbols [Dem 2002]. (c) Dynamics of Hubbard peak normalized intensity of 1T-
TaS2 in Mott-insulator state [Per 2006]. (d) Shift of the Hubbard peak that recovers in ps
time scale [Per 2006].........................................................................................................30
Figure 3.1.1 Diffraction. (a) Elastic scattering from two planes consisting identical atoms. Vectors ki
and kf are the incident and scattered wave vectors. (b) Momentum transfer, s, being the
vectorial change of incident and scattered wave vector, while θsc is the angle between
incident and scattered wave vectors....................................... ........ ......34
Figure 3.1.2 Scattering process. (a) Generic schematic layout and notation of scattering process. (b)
An electromagnetic plan wave polarized with its electric field along the z axis forces an
electric dipole at the origin to oscillate [AN 2001]............................................................36
Figure 3.1.3 X-ray scattering event from (a) an atom, (b) a molecule, and (c) and a crystal [AN
2001]........................................................................................................................ .37
Figure 3.2.1 Equipments for sample preparation. (a) CeTe3 sample glued to the copper grid. (b)
Custom grinder for thinning the sample. (c) Gatan 691 Ion Milling Machine.................43
Figure 3.2.2 TEM observation on CeTe3. (a) Ion-milled opening at CeTe3 sample. (b) CeTe3 film at
the edge of the opening. The central dark spot is a burn mark on the CCD camera. (c)
TEM diffraction image of CeTe3. The satellite peaks appear on the two sides of the
Bragg reflection along c* direction (circled in red), while the main Bragg peaks, circled
in blue, show square-symmetry along both a* and c* axes. (d) EDS element analysis of
CeTe3 sample showing ~1:3 ratio of Ce:Te. The Carbon trace was contributed to the
diamond lapping film used in the initial thinning of sample. The Copper trace was
originated from the cooper TEM grid the CeTe3 was glued on.........................................44
Figure 3.2.3 Thickness map on CeTe3. (a) TEM picture taken without energy filter. (b) TEM picture
taken with energy filter that blocks out energy-lost electrons. (c) Thickness map
processed using (a) and (b). The scale bar in (c) also applies to (a) and (b). (d) Typical
EELS from CeTe3 material. (e) Thickness profile of ion-milled CeTe3. ........................45
Figure 3.3.1 Experiment setup. (a) Layout of ultrafast electron crystallography apparatus. (b)
Schematic diagram of the proximity-coupled femtosecond electron gun.........................48
Figure 3.3.2 Experiment setup. (a)The electron pulse-length as a function of the number of electrons
per pulse employed. (b) Diffraction pattern of CeTe3 obtained from UEC setup.............49
Figure 4.1.1 Parameters of RETe3 family. (a) Energy density at Femi level as a function of the lattice
parameter of RETe3. (b) CDW gap size in various RETe3 material [Bro 2008]. (c) CDW
phase transition temperature in RETe3 where heavier RE element exhibit two CDW
transition temperatures [Ru 2008].....................................................................................52
Figure 4.1.2 Parameters of CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal
lattice. The lattice constant 4. 4 2 .0 and 4.40 (b) The real-space
model of corrugated CeTe slab (gray/red) and Te net (red) viewed along the b-axis. The
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coupling from px and py orbital chains from Te is also included. (c) An almost square
Fermi surface calculated from a tight-binding model with extended or reduced Brillouin
zone, as well as two sets of 1D bands from coupling of px and py chains........................53
Figure 4.1.3 Fermi surface of CeTe3. (a) Fermi surface of CeTe3, calculated from a tight-binding
model, consists the coupling from px (red), py (blue), and the limits of extended or
reduced Brillouin zones [Ru 2008]. (b) Fermi surface of CeTe3 measured from APRES
(solid black line) [Bro 2004]..............................................................................................54
Figure 4.2.1 Experiment result on CeTe3. (a) Crystal structure of CeTe3 with the corresponding
reciprocal lattice assignment with a=4.384Å, b=26.05Å, and c=4.403Å [Mal 2005]. Our
femtosecond (fs) electron pulse is directed along the b-axis, producing a transmission
diffraction pattern, while the fs laser pulses excite the sample area at 45o angle. (b) The
top panel shows the 3D diffraction intensity map, where the CDW satellites are located at
a*± Q0 in the dashed region. The lower panels display the temporal evolution of ultrafast
electron crystallography patterns subtracted by the equilibrium state pattern taken before
fs laser excitation (t < 0) to showcase the induced changes. The panels show both the ps
sequences for Bragg reflections and fs-to-ps sequences in a scaled-up view of the region
near CDW satellites.....................................................................................56
Figure 4.2.2 Dynamics of CeTe3. (a) The normalized Bragg peak intensity at q=-4a* and 4c* under
three different laser fluences: F=2.42, 4.62, and 7.30 mJ/cm2. The error bars are based on
electron counting statistics. (see Appendix A). (b) The normalized satellite intensity at
qcdw=3a*+Q0 shows a nonscalable two-step suppression..............................................58
Figure 4.2.3 Dynamics of CeTe3. (a) Detailed view of satellite intensity change at early times showing
a two-step suppression, along with the two-component fits. The data from F=2.43
mJ/cm2 are multiplied by 3 in order to compare with data from F=7.30 mJ/cm
2. The
dashed curve shows the fitted result for F=7.30 mJ/cm2 data. The error bars are
calculated based on the counting statistics. (b) The fast component of the satellite
suppression , showing a fast decay and recovery. The inset shows the amplitude of
the fast and slow
components extracted from fitting..................................59
Figure 4.1.4 Order parameter of CeTe3 CDW. (a) the temporal evolution of the structural order
parameter . The reduction of represents symmetry recovery as described by the CDW
potential evolving from double well to single well (insert). (b) The CDW collective
mode fluctuational variance , deduced from anisotropy analysis. (c) CDW
fluctuation amplitude order parameter correlation plot.........................................61
Figure 4.2.5 Conceptual framework of the three-temperature model (TTM). See text for notation....64
Figure 5.1.1 Structure of 1T-TaS2. (a) The tantalum atom is located at center of six octahedrally
coordinated sulphur atoms. The lattice constant are 3.3649 Å and
5.8971 Å. [Spi 1997]. (b) The Star-of-David 13-atom cluster representing the unit cell of
C-CDW in real space. The lattice distortion within each star is coupled with a strong
charge density redistribution. The angle between the CDW vector and lattice vector
is 13.9o...........................................................................................................................69
Figure 5.2.1 Phase diagram and diffraction pattern of 1T-TaS2. (a) Generic phase diagram of 1T-TaS2
under various physical domains (temperature, doping x, or pressure P ) reconstructed
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based on reference [Fau 2011] [Cav 2004] [Per 2006] The CDW phase evolution can be
characterized by the changes in the hexagonal CDW diffraction peaks at reciprocal vector
Q: Amongst the phase transitions starting from the C-CDW, the intensity of CDW and
the angle of Q (with respect to G) are reduced suddenly at the phase boundaries to
approximately half and 0 (from 13.9) to the IC-CDW (upper-right corner). (b) The
scale-up view of the ultrafast electron diffraction pattern, showing the hexagonal
diffraction patterns of C-CDW (Q) surrounding the lattice Bragg peaks (G)...................72
Figure 5.2.2 Transitions of 1T-TaS2 upon heating, showing complementary changes in the resistivity
1991].........................................................................................................75
Figure 5.2.3 Typical dynamics of Bragg and satellite (CDW) peaks of 1T-TaS2. Dynamics of each
components have been normalized and scaled for comparison.........................................76
Figure 5.2.4. Comparison between the thermal and optically induced changes of over absorbed
energy density (see section 5.3.4 for calculation). The temperature of 1T-TaS2 is at 150K
initially............................................................................................................77
Figure 5.2.5 The optically induced evolution of CDW states characterized by CDW suppression (in
ratio, based on unperturbed CDW intensity) and orientation angle at various absorbed
photon density for two different pumps: 800 and 2500 nm..............................................78
Figure 5.2.6 The temperature – photon-density phase diagram of 1T-TaS2.........................................80
Figure 5.2.7 The dynamics of CDW state transformations inspected via the rotation of CDW wave
vector Q away from C-CDW and the suppression of ICDW(t) [in ratio based on the ICDW(-
10 ps)]. The solid lines are drawn based on fitting the stair-case rises using a Gauss Error
function...............................................................................................................81
Figure 5.2.8 Cartoon depiction of the dynamical evolution CDW states in a zig-zag pathway over the
free energy contour defined by the changes in and A2 based on the dynamics extracted
from (A). A is scaled to 0.15Å at C-CDW state based on reference [Spi 1997]...............83
Figure 5.3.1 Optical images of 1T-TaS2. (a) Optical picture of cleaved 1T-TaS2 from bulk as a
starting piece for exfoliating. (b) 1T-TaS2 on scotch tape after exfoliated once. (c)
Optical image of peeled 1T-TaS2 sample taken with light coming from below the sample
stage. (d) 1T-TaS2 samples after multiple "peeling"........................................................86
Figure 5.3.2 Optical images of 1T-TaS2 samples. (a) Thin 1T-TaS2 samples on silicon surface. (b)
1T-TaS2 samples on TEM grid ready for UEC experiment...............................................87
Figure 5.3.3 Diffraction pattern of 1T-TaS2. (a) Diffraction pattern of 1T-TaS2 in the NC-CDW state
taken at room temperature. The image is in logarithmic scale to make CDW peaks more
visible. (b) Scale-up view of the diffraction pattern from the square region in (a), showing
clear hexagonally distributed first-order CDW satellite peaks around the central lattice
Bragg peaks. Second-order CDW satellite peaks are also visible. (c-e) Time-dependent
diffraction images from a single Bragg peak region at different time delays: -1ps, +1ps,
+3ps respectively. The solid line connects neighboring Bragg peaks, representing the
direction of the lattice vector G. The dashed line connects neighboring CDW peaks,
representing the direction of the CDW vector Q. ϕ represents the angle between CDW
xiv
and Bragg vectors. In (e), CDW vector rotates fully into the lattice vector direction,
indicating that the NC-CDW is transformed to IC-CDW by 3 ps....................................89
Figure 5.3.4 The determination of CDW phase boundaries based on presence of a step or a slope
change................................................................................................................................90
Figure 6.1.1 Purposed structure of water (a) LDL and (b) HDL [Cha 1999]..................................94
Figure 6.1.2 Optical studies on water (a) comparison of g(r) of liquid water measured at 7, 25, and
66oC with X-ray. (b) Raman spectra with 3115 cm
-1 pumping, fit using the two Gaussian
sub-bands V(red) and V(blue). (c) Time dependence of red and blue band with 3115 cm-1
pumping at different temperature.......................................................................................95
Figure 6.2.1 Experiment setup. (a) Experiment setup for ice/water related experiment. Different
diffraction geometry and corresponding water diffraction image obtained on CCD camera
in reflection diffraction setup and (b) transmission diffraction setup................................98
Figure 6.3.1 OH vibration modes of water. (a) Illustration of three vibration modes in OH bond of
water. (b) Experimental observed frequency for OH vibrations in water [For 1968]. The
corresponding wavelength for some frequency is listed in red........................................101
Figure 6.3.2 Different nonlinear process. (a) Geometry of sum-frequency generation. (b) Energy-level
description of SFG. (c) Geometry of difference-frequency generation. (d) Energy-level
description of DFG [Boy 2003].....................................................................................103
Figure 6.3.3 Optics path and setup for mid-IR generation. The green line indicates the 1256 nm optical
path. Red line represents the 2165 nm laser path. The blue path is where the 3000 mid-
IR travels. The M1 to M7 mirrors are purchased for the high reflection on 1256 nm and
2165 nm, while M8-M12 are Au coated exhibiting low loss for the infrared range. The
purple arrows indicate the polarization of each wave................................................105
Figure 6.4.1 The water sublimation measured by from QMS as temperature rises with different dosing
time..................................................................................................................................108
Figure 6.4.2 The pure silicon mounted on sample holder (a) before and (b) after water dosing. (c)
Optical image of thin amorphous silicon membrane (blue area) manufactured on a silicon
substrate (grey background). (d) Thin amorphous silicon membrane sample mounted
(circled in red) onto our sample holder ready for transport into our UHV chamber for
transmission diffraction experiments...........................................................................109
Figure 6.4.3 Pictures from water experiment. (a) The diffraction pattern from AuNP decorated silicon
substrate at room temperature. (b) When the amorphous water starts to cover the AuNP
and obscure the AuNP diffraction, water dosing can stop, taken at T = 115 K. (c) A few
hours after water dosing is stopped, the amorphous water self-assemble into crystal form
at 115 K. (d) Diffraction pattern from silicon with nanocavity at room temperature. (e)
Scattering from water starts to replace the nanocavity pattern, taken at T = 78 K. (f)
Fully crystallized water completely cover the Si substrate with nanocavity, taken at T =
127 K. (g) Diffraction pattern of ice yields to that from Si nanocavity when ice starts to
sublimate at T = 157 K. (h) The diffusive diffraction pattern from amorphous silicon
membrane at T = 115 K. (i) Diffraction pattern from ice and amorphous silicon
membrane. (j) SEM image of nanocavity on silicon substrate.......................................110
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Figure 6.5.1 Reflective diffraction experiment on water. (a) Reflective diffraction geometry with ice
deposited on pristine silicon and typical diffraction pattern from ice layer. (b) Intensity
ratio dynamics of ice (111) + (200) triggered by 3000nm laser, f = 4.5mJ/cm2, at T =
130K.................................................................................................................................112
Figure 6.5.2 Transmission diffraction experiment on water. (a) Geometry of transmission diffraction
experiment. (b) Diffraction profile obtained before (red curve) and 2 ps after (blue curve)
the excitation laser hits the ice sample. The +2ps profile has been scaled to compare with
that before mid-IR lands on sample.................................................................................113
Figure 7.1.1 Charge redistribution at interface after photoexcitation. (a) dielectric realignment. (b)
carrier diffusion. (c) interfacial charge transfer..............................................................117
Figure 7.2.1 The slab model for transient surface voltage...................................................................119
Figure 7.3.1 Charge redistribution spectrum. (a) Surface photovoltage response map constructed
using the diffractive voltammetry conducted on the water-ice surface covering gold
nanoparticles/SAM/silicon interface at excitation wavelength from 400 to 800nm. Four
selected surface photovoltage shown in white curves, at = 400, 470, 525, and
585nm, demonstrate a composition of two dynamics with different timescales. (b)
comparisons between the surface voltage response spectra obtained from the interface
without the coverage of water-ice (black line), ones with water-ice layer showing a red
shift of the resonance peak (green line) at 30ps, and the bifurcation of peaks (blue line) at
100ps...................................................... .....................................................121
Figure 7.3.2 Dynamics of induced charge. (a) The controlled experiment with the presence of AuNP
for Ice/AuNP/SAM/Si photovoltage measurement. The rise of the surface voltage is
delayed by the timescale of the charge carriers migrating to the ice surface after being
generated from the Si substrate. (b) Equivalent results obtained the surface with AuNP
decoration. By comparing to (a), we can deduce the fast components (blue circles)
unique to the nanoparticles-decorated surface.................................................................123
Figure A1 Analysis on electron count. (a) The discrete single-electron events recorded on a CCD
camera. (b) The number of occurrences of single-electron events as a function of digital
counts recorded for these events. A mean value of 989 is determined as the analogue-to-
digit unit, used to convert the CCD signals into the electron counts...............................128
Figure A2 Statistic on electron counts. (a) The data integration time used for each time stance under
laser fluences F=2.43, 4.67, 7.30 mJ/cm2. (b) The absolute integrated intensity evolution
of CDW superlattice peak in unit of electron counts. (c) The absolute
integrated intensity evolution of main lattice peaks at (0,4) extracted from the
same diffraction images as (b).............................. ..................................................129
Figure B1 The zoomed in plot of satellite intensity of CeTe3 at early times showing two-step
suppression. The data from F=2.43 mJ/cm2 are multiplied by 3 to compare with data from
F=7.30 mJ/cm2. The error bars are calculated based on the counting statistics described
in Appendix A...............................................................................................................130
Figure B2 Two component fit. (a) The results of two component fit of experimental S1(t)/ S1(t<0)
data at F=7.30 mJ/cm2 (blue: total, red: first component, black: second component). (b)
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The value as a function of =A1/A2 based on fitting S1(t)/ S1(t<0)..........................132
Figure C1 Images of MWCNT. (a) Suspended MWCNT on copper TEM grid. (b) TEM image of a
suspended MWCNT on TEM grid. (c) SEM image of a MWCNT deposited on holey
carbon TEM grid. (d) SEM image of a MWCNT deposited on holey carbon TEM grid.
(e) Diffraction pattern from a MWCNT. (f) Individually separated MWCNT on thin Si
membrane................................................................................................134
Figure D1 Tsunami fs configuration.................................................................................................135
Figure D2 Two IR images on M4...................................................................................................136
1
CHAPTER 1
Strongly Correlated Complex Materials
Complex materials can be characterized as having no dominant energy scale; hence, the
interaction between various degrees of freedom, like charge, lattice, orbital, and spin can greatly influence
and determine their functionality. This strong interplay between subsystems often leads to emergent
properties, like colossal magnetoresistance, high-temperature superconductivity, and spin- or charge-
density waves. To disentangle the coupling between these subsystems, ultrafast pump-probe techniques
offer a glimpse of how the material responds after it has been disturbed. From the material response, we
can learn the sequence, magnitude, and role of between each player in the system in such emergent
properties.
In this chapter, a survey of the literature on strongly correlated systems investigated by ultrafast
technique is presented, sans the charge-density wave materials which will be reserved for Chapter two.
2
1.1. Colossal Magnetoresistance Manganites
Magnetoresistance, the change of a material’s resistivity with the application of a magnetic field,
was recognized more than 150 years ago, most notably by W. Thomson in 1856 [Tho 1856] when he
measured the resistance of iron and nickel in the presence of a magnetic field. Later, in 1950, Jonker and
van Santen found that the perovskite LaMnO3, an antiferromagnetic insulator, becomes metallic when La
is substituted by Sr. When the substitution is around 30%, this hole-doped system displays an insulator-
to-metal transition and ferro- to antiferromagnetic transition upon cooling [Jon 1950]. The application of
magnetoresistance got a significant boost when giant magnetoresistance (GMR), a change in resistivity of
more than 50% at low temperature [Bai 1988] or ~1.5% at room temperature [Bin 1989], was discovered
by Albert Fert and Peter Grünberg. In the 1990s, R. von Helmolt et al. [Hel 1993] and Jin et al. [Jin
1994] coined the term colossal magnetoresistance (CMR) as they reported an orders-of-magnitude change
in resistivity in manganite perovskites (Fig. 1.1.1). With the possibility of applications in magnetic field
sensors, like those in hard disk drives, biosensors, and microelectromechanical systems, CMR remains a
highly active field of research.
In 1951, to explain the simultaneous occurrence of ferromagnetism and metallicity found by
Jonker and van Santen, Zener proposed the “double exchange” mechanism, predicting the electron
movement from one species to another can be facilitated more easily if the electrons do not have to
change spin direction when on the accepting species. The electron’s ability to delocalize reduces its
kinetic energy. The overall energy saving can lead to ferromagnetic alignment of neighboring ions [Zen
1951]. However, in 1996, Millis et al. [Mil 1996] and Roder et al. [Rod 1996] suggested the double
exchange theory cannot explain the magnitude of change in resistivity at the ferromagnetic transition, and
proposed that an electron-phonon coupling contribution, or a strong implied by the Jahn-Teller coupling,
must be included in the Hamiltonian.
To provide some insight on this discussion, Averitt et al. [Ave 2001] utilized ultrafast optical
spectroscopy to show the relative contributions of spin fluctuations and phonons in determining the
3
Figure 1.1.1 Previous studies on CMR. (a) Magnetoresistance measurement at room temperature for La-
Ba-Mn-O thin films. (b) Temperature dependence of resistivity (R), resistivity (), and magnetization (M)
of La-Ca-Mn-O films.
conductivity in La-Ca-Mn-O and La-Sr-Mn-O ~100nm thin films. Using terahertz pulses to measure
conductivity of the material after optical excitation, Averitt and coworkers observed a two-step transient
response (Fig. 1.1.2). They attributed the fast, 2 ps, initial conductivity decrease to the change in phonon
temperature as the optically excited electrons relax through electron-phonon coupling. To model the
second step in the dynamics, they used a two-temperature model to describe the energy transfer between
the phonons and spins after the initial increment of phonon temperature. The results from their two-
temperature model were extended to quantify the contribution of the temperature change of spins and
phonons to the change in conductivity (Equ. 1.1.1):
1.1.1
where Tp and Ts being temperature of phonon and spin while being conductivity. From this analysis,
they concluded the conductivity is primarily determined by thermally disordered phonons at low
temperature while spin fluctuations dominate closer to Tc, as shown in Fig1.1.3(a).
It has been shown that there is charge ordering in doped manganites, and this charge ordering has
been interpreted as the localization of charge at atomic sites, or a “tolerance factor” involving the effect of
(a) (b)
4
Figure 1.1.2 Previous studies on CMR. (a) Induced change in transmitted electric field. (b) Induced
change in real conductivity.
static crystal structure on electron hopping, as shown in Fig.1.1.3(b) [Mil 1998]. However, Cox et al.
[Cox 2008] showed that the charge ordering in 0.5 doped La-Ca-Mn-O manganites has similar signatures
of collective transport in impurity-doped charge-density wave (CDW) systems. From their observations
under TEM, La0.5Ca0.5MnO3 has satellite peaks appearing only in the direction parallel to the superlattice
direction, shown in Fig. 1.1.3(c). At the same time, resistivity measurements also show typical
signatures of pinned and sliding states seen in anisotropic CDW systems, as shown in Fig. 1.1.3 (d) and
(e). The similarity of electron-lattice properties between GMR, CMR and CDW materials shows the
complex yet universal phenomenon in strong correlated electronic systems.
(a) (b)
5
Figure 1.1.3 Previous studies on CMR. (a) Contribution of spin and phonon to conductivity at different
temperature (b) Phase diagram of La1-xCaxMnO3 showing phases including charge-ordering (CO),
antiferromagnet (AF), canted antiferromagnet (CAF), ferromagnetic (FM), and ferromagnetic insulator
(FI). (c) Line scan of TEM images in the a (red line) and c (blue line) showing the satellite peaks only
present in the a direction. (d) and (e) Differential resistivity versus d.c. bias applied in the a (red lines)
and c (blue lines) directions at various temperatures.
(a) (b)
(c) (d) (e)
6
1.2. Cuprate Superconductors
Similar to materials supporting CDWs, high-temperature superconductors (HTSC) are another
class of strongly correlated systems in which the interplay between spin, charge, lattice, and orbital
degrees of freedom play important roles. The division between CDW and HTSC systems became even
more blurry when the charge-ordered “checkerboard” state was observed in cuprates [Han 2004], and
when superconductivity emerged from a CDW material, 1T-TaS2 [Sip 2008]. With ultrafast techniques,
the possible cooperation or competition between CDW and HTSC can be further explored.
In 2007, Gedik and coworkers explored the superconducting phase transition in oxygen-doped
La2CuO4+ with ultrafast electron crystallography [Ged 2007]. By observing the shift of diffraction
intensity of a Bragg peak from one side of a point of constant intensity in momentum space to another, i.e.,
as for an isosbestic point, the spectral position where two interconverting species have equal absorbance,
they attributed this phenomenon to a phase transition in which optical excitation induced a charge transfer
from oxygen to copper in the copper-oxygen planes leading to lattice distortion, as shown in Fig. 1.2.1 (a).
At the same time, by inducing this phase transition with optical excitation at different fluence, they
observed that the photon-doping threshold, the number of absorbed photons per copper site, is very
similar to the fractional charge per site required to induce superconductivity, as shown in Fig. 1.2.1 (b).
This report demonstrated that ultrafast electron crystallography can be an ideal tool to explore phase
transitions in strongly correlated systems. It also implied that optically induced carrier doping may be
closely related to chemical doping, and hence signify the prospect of light-mediated control of phase
transformations.
In 2008, Kusar and coworkers utilized an optical pump-probe technique to study the energy
landscape of the superconducting condensate in La2-xSrxCuO4. By observing the change of photo-induced
reflectivity with different optical excitation fluence, they deduced the energy density required to vaporize
the superconducting state is significantly higher than the thermodynamically measured condensation
energy density. Together with the estimated spin-lattice relaxation time being orders longer
7
Figure 1.2.1 Previous studies on cuprates. (a) Diffraction intensity crossing a common point at different
delay time at different fluence. (b) Threshold in fluence that would initiate the phase transition. (c)
Typical photoemission data at Fermi surface showing change in electron dispersion and spectra after
optical excitation. (d) Dynamics of superconducting gap magnitude at two locations.
than the vaporization time observed in the experiment, they attributed the vaporization of condensate to
phonon-mediated pair-breaking. Together with the work done by Torchinsky et al. [Tor 2013] observing
the charge-density wave fluctuation in cuprate superconductors, it demonstrated that ultrafast optical
pump-probe techniques may distinguish the pathways and mechanisms of phase transitions through
spectral and dynamic information.
Time-resolved angle-resolved photoemission spectroscopy (tr-APRES) was employed by
Smallwood et al. in 2012 to investigate the Cooper pair recombination time at different locations of the
superconducting gap in Bi2Sr2CaCu2O8+ [Sma 2012]. By observing the shift of spectral weight across
(a) (b)
(c) (d)
8
the Fermi surface, Smallwood and coworkers monitored quasi-particle creation and recombination at
different momenta, as shown in Fig. 1.2.1 (c). Meanwhile, from the spectral peak shift, they deduced the
dynamics of formation of the superconducting gap at different locations in the superconducting gap ,
shown in Fig. 1.2.1 (d).
From these results, they suggested that the momentum-dependent recombination of Cooper pairs
can be due to the quasiparticle energy and momentum approaching resonance with charge or spin density
wave fluctuations. With tr-APRES, the dynamics at the Fermi surface can be readily explored, adding
more information on the electronic correlations in the system.
9
1.3 Experimental Challenges
Among the ultrafast techniques reviewed in the last section, ultrafast optical pump-probe
techniques offer the high signal-to-noise ratio and relative ease of implementation. However, optical
observations are often limited to the electronic response; hence, interpretation of the data can be difficult
at times. While tr-APRES offers direct observation of electronic distributions in materials, it can be
limited to information at the surface due to the relatively short penetration depth of low-energy electrons.
Similar to optical pump-probe spectroscopy, tr-APRES offers only indirect observations of the lattice
subsystem. Ultrafast X-ray diffraction techniques offer atomic information after optical excitation,
however, it’s long penetration depth often limits the observation to bulk materials and relatively long
experiment times.
Ultrafast electron crystallography is suitable for obtaining atomic information, thanks to its
sensitivity to lattice periodicity. Meanwhile, the typical nanometer-long penetration depth of high-
energy electrons is ideally matched to the optical penetration depth for pump-probe studies. However, in
order to obtain shortest time-resolution, it is crucial to have samples prepared with a high uniformity over
similar length scales.
10
CHAPTER 2
Charge-Density Waves Materials
This chapter presents some basics theoretical descriptions of charge-density waves (CDW)
materials, the studies that investigate CDW with various techniques, and scientific open questions we
wish to study and answer. Since the formation of CDW is the central argument in literature [Wil 1975]
[Frz 1979] [Gru 1994], we would start the discussion with simple description on the electronic aspect of
low dimensional system and the derivation of the Lindhard function in general. Then we discuss the
instability in electron gas of low dimension, the related the phenomena like Kohn anomaly and Perierls
transition, and the collective modes of CDW in brief. With an overview of past studies on CDW
examined by various ultrafast techniques, we can discuss the results and implications from these previous
works, as well as the prospects our ultrafast electron crystallography technique can bring to the discussion,
and possibility provides some answers for some open questions.
11
2.1 Overview of Charge-Density Waves
Charge-density waves can develop in low-dimensional metals due to the interaction between
electrons and phonons. The resulting ground state exhibits a periodic charge density modulation with a
periodic lattice distortion with both periods related by a wavevector that can be traced to Fermi-
surface nesting [Grü 1994]. The CDW state originates from the reduced electronic dimensionality of the
parent compound. Therefore we start with the simplest case, a one-dimensional metallic material, to
introduce some basics of charge-density waves.
2.1.1 Nearly Free Electron in One-dimensional Conduction Band
Using the free-electron model, where the only electron-lattice interaction is the electron
confinement via the lattice to a 1D potential well, we can derive the electron dispersion relation,
, (2.1.1)
as shown in Figure 1a, in terms of wavevector , electron mass , and reduced Planck's constant . [Kit
2004]. However, in order to describe the electron properties better in various metals, semi-metals, or
semiconductors, it is essential to include the weak perturbation of band electrons due to the periodic
potential of the ion cores. This nearly free electron model can be rationalized by treating the valence
electrons within a crystal as affected by diffraction from the lattice just as if they had been incident from
the outside [Zim 1979]. In 1958, A.V. Gold first used this nearly free electron approximation, assuming
that the conduction electrons are free except at the zone boundaries due to Bragg reflection from a
periodic potential, to explain the band structure of lead, which has four valance electrons outside the filled
5d10 shell and 78 out of the 82 total electrons in the ion core [Gol 1958].
The band structure of nearly free electrons exhibits an energy gap at the zone boundary of the
lattice, as illustrated in the first Brillouin zone in Figure 1b. With the Hamiltonian
12
, (2.1.2)
Figure 2.1.1 Band structure of two electron models. (a) Energy versus wavevector for a free electron
(b) Energy versus wavevector, or band structure, for an electron in a monatomic linear lattice of lattice
constant [Kit 2004].
the magnitude of the band gap of the 1D nearly free electrons can be approximated by using as a
perturbation the periodic lattice potential
(2.1.3)
where is the shortest wave vector in the reciprocal lattice, and is the lattice constant. The
matrix elements of using a plane wave representation are
(2.1.4)
Using degenerate perturbation theory, we find the energy at the first Brillouin zone boundary k = π/a of
the states and . The secular determinant is
. (2.1.5)
(a) (b)
13
Since at the boundary, Equation (2.1.5) reduces to
or
. (2.1.6)
Hence the band gap at , is simply related to the periodic lattice potential (2.1.3) [Kit
1963]. The band gap calculated in this way, together with the nearly free electron assumption, provided a
more accurate model for understanding insulator, semimetal, metal, and semiconductor.
2.1.2 The Lindhard Response Function of an Electron Gas
For analyzing CDW materials, we shall examine the effect of a weak time-dependent potential
acting on the free electron gas. We start with the Schrödinger equation for an electron
experiencing an external potential :
(2.1.7)
In the case of , we have
(2.1.8)
where
and volume of the system. The time-dependent perturbing potential is introduced as
, (2.1.9)
where the complex conjugate (c.c.) ensures no additional Fourier components are introduced and α→0+
enables the perturbation to be switched on adiabatically.
The change in charge density and the perturbed potential can be related via the susceptibility
where
, (2.1.10)
(2.1.11)
and
(2.1.12)
14
By applying the time-dependent first order perturbation formalism to (2.1.7), using
, (2.1.13)
and performing some rearrangements, we get
(2.1.14)
Using (2.1.9), we can expand the right-hand side of (2.1.14) as
, (2.1.15)
which gives us
(2.1.16)
and
(2.1.17)
With the wave function, we can determine the induced change in electron density:
2.1.1
2.1.1 b
In (2.1.18a) to (2.1.18b), is the Fermi-Dirac distribution, and the spin degeneracy provides the
factor of 2. We can also substitute with and with in the second term in (2.1.18b) since it
is summed over all occupied values. This leads to
2.1.19
Comparing to (2.1.19) and (2.1.12), we obtain
15
Figure 2.1.2 Responses in different dimensions. (a) The Lindhard response function for different
dimensions. (b) and (c) The Fermi surface, noted in red lines, and Fermi nesting, the condition of a
common paring wavevector at the Fermi surface. (d) The pairs of one full and one empty state can be
connected by the wavevector .
2.1.20
If we replace the summation with an integration and a static potential, or and , we obtain the
following result
2.1.21
where is the dimension of the system. If we consider a 1D system with length of the system,
electron mass, and number of free electrons at , (2.1.21) becomes the Lindhard response
function, first derived in [Lin 1954],
2.1.22
2.1.2
(a) (b) (c)
(d)
16
2.1.24
where the density of states
, Fermi energy
, and Fermi wave vector
with the assumption of a linear dispersion relation around the Fermi energy
.
For the case of in (2.1.21), the two Fermi distributions in the numerator cancel out except
when or . This means the most significant contributions to the integral
(2.1.21) come from pairs of occupied and unoccupied states, each of each of which has almost the same
energy so that the denominator can be very small. Also, the paired states differ by so the Fermi
distribution in the numerator does not cancel out, as illustrated in Figure 2.1.2(d). This divergence of
at in 1D can also be observed in (2.1.24), which is plotted along with higher dimensional
cases in Figure 2.1.2(a), known as Peierls instability [Pei 1956]. Together with equation (2.1.10), it
implies that an external perturbation leads to a divergent charge distribution and suggests the electron gas
itself is unstable with respect to the formation of a periodical electron charge distribution. The period of
this charge variation is related to by
2.1.2
The divergence of the response function at can be related to the topology of the Fermi
surface. For an extremely anisotropic 1D metal, the Fermi surface contains two lines that can be
connected by a common wavevector , as illustrated in Figure 2.1.2(b), and is commonly referred
to as perfect Fermi nesting. In this condition, the electrons can scatter efficiently into unoccupied states
and change their wave vector by . However, in higher dimensions, as in the 2D Fermi surface shown
in Figure 2.1.2(c) and the response function in a 3D case [Dre 02] plotted in Figure 2.1.2(a),
2.1.2
the number of paired states reduces significantly and thereby removes the singularity of at .
17
Figure 2.1.3 Low-dimensional gas. (a) Fermi surface of a quasi-one-dimensional electron gas [Grü 1994].
(b) The response function of a one-dimensional electron gas at various temperatures [Hee 1979].
In the case of a quasi-one-dimensional metal, like CeTe3 presented later in this thesis, the Fermi
surface can be modeled by introducing a dispersion in the direction perpendicular to the direction along
which the response function is evaluated [Grü 1994]. Starting from a two-dimensional dispersion relation
2.1.27
where a and b are the lattice constants in the x and y directions respectively, the quasi-one-dimensional
dispersion relation close to the Fermi energy can be deduced by using and the linear dispersion in
the x direction:
2.1.2
The Fermi surface obtained by calculating from (2.1.28),
2.1.29
exhibits a sinusoidal topology in the plane, as shown in Figure 2.1.3(a). Compared to the 2D case,
the Fermi surface of a quasi-one-dimensional electron gas contains more electron pairs with similar
energies, and the nesting condition is associated with the wave vector . The response
(a) (b)
18
function exhibits a singularity at . In the two-dimensional phase space, the singularity
corresponds to a periodic modulation with a wave vector and Perfect nesting
condition in the quasi-one-dimensional case is possible only in the case when , and should be
applicable to materials with strong anisotropy of the single particle bandwidth. As increases, the
contribution from the third term in (2.1.29) becomes more significant and the singularity in is
gradually removed, as illustrated in Figure 2.1.3(b).
The temperature-dependence of the one-dimensional response function can be approximated
linearly near , or around , by introducing with and to the
numerator of (2.1.21), which yields
2.1. 0
This leads to
2.1. 1
2.1. 2
where is an arbitrarily chosen cutoff energy that is usually close to . As in [Sol 2002], this finite
temperature dependence of in 2D can be derived by calculating the grand canonical ensemble of
the structure function. The temperature-dependent response function suggests that we can expect a phase
transition as the temperature crosses the Peierls critical temperature.
2.1.3 Instabilities in a One-Dimensional Electron Gas
Relying on the notion that the external potential leads to a density fluctuation , we
can examine various one-dimensional metasl by incorporating a potential induced by the change
in density ,
2.1.
19
States Pairing Total Spin Total Momentum Broken
Symmetry
singlet superconductor electron-electron gauge
triplet superconductor electron-electron gauge
charge-density wave electron-hole translation
spin-density wave electron-hole translation
Table 2.1.1 Various broken-symmetry ground states of one-dimensional metals [Dre 2002].
where is a -independent coupling constant, and and are the spatially dependent Fourier
components of potential and density fluctuations, respectively. With (2.1.33) and
replaced in (2.1.10), we obtain the induced density fluctuation
2.1. 4
From (2.1.34), we can see a system would reach an instability with a finite induced density fluctuation
and when
2.1.
For a rough estimate, we can plug (2.1.32) into and obtain the mean field transition
temperature
2.1.
Various fundamental condensates, e.g. superconductor, charge-density wave, and spin-density
wave, present a stark contrast in sub-system interactions, paring of quasi particles and broken symmetry,
yet many of their properties show similar presentation. It is vastly interesting to see that some materials,
like 1T-TaS2 reported later in this thesis, can exhibit more than one condensate when conditions change.
The occurrence of these states can be decided by a combination of electron-phonon interaction coupling
constant and electron-electron interaction coupling constant , which represent the interaction with
momentum transfer of and , respectively [Grü 1994]. Some of the properties of these broken-
symmetry ground states are listed in Table 2.1.1.
20
The two superconducting states in Table 2.1.1 both develop in response to a interaction with total
momentum , which is commonly known as particle-particle channel or Cooper channel. With a
pairing that results in total momentum , it produces the charge-density wave or spin-density wave
via the particle-hole channel, or the Peierls channel. For all these condensates, the order parameter is
complex,
2.1. 7
For superconducting states, the gauge symmetry is broken while the phase is invariant under a gauge
transformation. On the other hand, the two density-wave ground states exhibit broken translational
symmetry. The collective excitations of these two density-wave ground states are called phasons and
amplitudons, as they are related to changes in the phase and amplitude, respectively,m of the condensate
order parameter. The amplitude is related to the single particle gap that appears at in the case of
density waves [Grü 1994].
2.1.4 The Kohn Anomaly and the Peierls Transition
In order to describe the charge-density wave and its transition, a Hamiltonian that includes the
electron-phonon interaction is needed. For this purpose, the Fröhlich Hamiltonian [Fro 1954] is
commonly used. Here it is written in the second quantization formalism
2.1.
The first term in (2.1.38), the Hamiltonian for the electron gas, includes the creation and
annihilation operators, and respectively, for the electron state with energy . The
phonon system is described by the second term in (2.1.38), , with the phonon creation and
annihilation operators
and , characterized by the wavevector . In terms of these
operators, the lattice displacement can be expressed as
21
2.1. 9
where is the number of lattice sites per unit length, is the ionic mass, and is the normal mode
frequency. At the same time, the normal coordinates of ionic motion can be described by
2.1.40
Finally, the third term in (2.1.38), which represents the electron-phonon interaction , contains the
electron-phonon coupling constant [Grü 1994]
2.1.41
With the Fröhlich Hamiltonian (2.1.38), we can describe the effect of the electron-phonon
interaction on the phonon frequency by establishing the equations of motion of the normal coordinates.
With a small displacement in coordinate, the equations of motion read
and
2.1.42
where is the second time derivative of the coordinate. Utilizing (2.1.10) and the commutation
relations of the normal coordinates and conjugate state momenta of the ionic motions, (2.1.42) becomes
2.1.4
where is the phonon frequency without electron-phonon interaction. From the equation of motion
(2.1.43), the renormalized phonon frequency is
2.1.44
The phonon frequency depends on the interatomic restoring force, which originates from
Coulomb interaction between the cores, for the corresponding lattice arrangement. When the lattice
distortion provides the electronic system with a potential, it induces charge redistribution, as presented
earlier in section 2.1.2. It is reasonable to imagine the induced charge-density wave reduces the restoring
22
Figure 2.1.4 The Kohn anamaly. (a) The Kohn anomaly of acoustic phonon frequency showing the Kohn
anomaly at temperatures above the mean field transition temperature. (b) Phonon dispersion relations of
1D, 2D, and 3D dimensional metals [Grü 1994].
force between cores through shielding effects. Therefore the phonon frequency should reduce, or soften,
known commonly as Kohn anomaly. By incorporating (2.1.32) as , the phonon frequency
becomes
(2.1.45)
As temperature decreases, , and we obtain the transition temperature at which the
phonon frequency is "frozen-in", or the Peierls charge-density wave transition temperature in the mean
field approximation,
2.1.4
Where is the electron-phonon coupling constant [Grü 1994]
2.1.47
When Taylor-expanding (2.1.45) at , we can determine the temperature-dependence of
as
(a) (b)
23
for
2.1.4
Using (2.1.44) and (2.1.48), we can plot the phonon dispersion relation showing the emergence of the
"frozen-in" phonon as in Figure 2.1.4(a).
The phase transition is defined by the temperature where , caused by the sharply
diverging response function of the 1D electron gas. For higher dimensions, however, the reduction of
phonon frequency is less significant, as shown in Figure 2.1.4(b), and is less dependent on the
temperature. Therefore, for a weak electron-phonon coupling, can remain finite at and there
is no phase transition.
Below the phase transition temperature , the renormalized phonon frequency is zero, leading
to the “frozen-in” lattice distortion. Macroscopically, this means the occupied phonon mode has finite
expectation values
. Therefore, we can define the order parameter (2.1.37) as
2.1.49
Combined with (2.1.39), we get [Grü 1994]
2.1. 0
with
2.1. 1
This means the increment in the elastic energy due to the lattice distortion can be expressed as
2.1. 2
or, when plugging in (2.1.50),
2.1.
where is defined in (2.1.47).
The Fröhlich Hamiltonian (2.1.38) becomes
24
2.1. 4
When considering and
, the Hamiltonian can be expressed as
2.1.
The electronic part of (2.1.55) becomes, with order parameter (2.1.49),
2.1.
With the dispersion relation , we consider only the states near Fermi level, and label
the states near and near with subscript 1 and 2 respectively. The electronic part of Hamiltonian
can be written as
2.1. 7
where substitutes for simpler notation One can use Bogoliubov transformation, typically used
in BCS theory, to diagonalize (2.1.57) with a new set of operators
and
2.1.
Using the constrain of
, (2.1.57) becomes
2.1. 9
It can be diagonalized if the coefficient of off-diagonal terms is zero, or
2.1. 0
We can satisfy the constrain
by choosing
and
2.1. 1
which leads (2.1.60) to
2.1. 2
25
Figure 2.1.5 The single particle band, electron density, and lattice distortion in (a) state above and
(b) in CDW state at . (c) The temperature dependence of band gap and the renormalized
phonon frequency . Both carries a characteristic dependence of
Plugging (2.1.62) into (2.1.61) then we get [Grü 1994]
and
2.1.
where
2.1. 4
Substituting (2.1.63) in (2.1.59), we obtain
2.1.
At the same time, the ground-state wave function can be written as
2.1.
where represents the vacuum. The periodic charge density variation can also be calculated in the
weak coupling limit [Grü 1994]:
(a) (b) (c)
26
2.1. 7
where is the constant electronic density in the metallic state.
The equilibrium lattice positions (2.1.50), the dispersion relation (2.1.64), and the electronic
density (2.1.67) are shown in Figure 2.1.5. Instead of the linear dispersion of a
metallic state, from (2.1.64) and (2.1.65) we can see the electron density of states disappears in the CDW
ground state and an energy gap opens at the Fermi level, . The 1D CDW material can become
an insulator upon the gap opening, but the 2D materials stay metallic due to the ungapped region of the
Fermi surface [Folge 1973] [Ru 2008]. The ground state, depicted in Figure 2.1.5(b), exhibits a periodic
modulation of the electron density, as well as the lattice position distortion, hence the term Charge-
Density Wave.
By minimizing the energy of (2.1.64), we can obtain the magnitude of the gap. The gap opening
lowers the electronic energy, which can be calculated by
2.1.
2.1. 9
By expanding the log term in the weak coupling limit, , (2.1.68) becomes
2.1.70
Combing (2.1.53), the total energy change in the CDW ground state is
2.1.71
If we minimize the total energy with a weak electron-phonon coupling, or , we obtain
2.1.72
Comparing with (2.1.36), we get [Grü 1994]
27
Figure 2.1.6 CDW states. (a) CDW ground state (b) Phase mode (c) Amplitude mode. The dotted lines
represents the electronic part of charge-density wave while the arrow indicates the displacement of ion
core, as red dots, from the equilibrium position.
2.1.7
At the same time, the condensation energy
2.1.74
Equation (2.1.73) follows the BCS relation between zero-temperature gap and the transition temperature.
At , thermally excited electrons can cross the band gap, screen the electron-phonon
interaction, reduce the energy gain, and eventually induce a phase transition. The temperature evolution
of the gap near , shown in Figure 2.1.5(c), can be derived [Tin 2004] as
2.1.7
The equation (2.1.73) is essentially the same as that describing the temperature dependence of the
superconducting gap using the framework of BCS theory [Sch 1964] [Tin 1975].
2.1.5 Collective Excitation of Charge-Density Waves
The charge-density wave excitation can be described by a complex order parameter (2.1.37),
therefore amplitude and phase modes should be expected. In the at limit, two phonon
dispersion relations of the charge-density wave have been derived by [Lee 1974]:
and
2.1.7
where
(a) (b) (c)
28
2.1.77
The two excitations in (2.1.76) are commonly referred as phase mode (phason) and amplitude mode
(amplitudon), and are sketched in Figures 2.1.6(b) and (c), respectively. When the phason and
, the CDW collective excitation corresponds to a translational motion without dissipation, which is
known as the mechanism of Peierls-Fröhlich superconductivity. However, this phenomenon is limited by
impurities in the lattice, or the pinning effect.
Since in the phase mode, the displacement of electronic charge distribution relative to the ionic
positions is involved, the phason is expected to be optically active. In contrast, this displacement is
absent in the amplitude more. Therefore amplitudon should be Raman active [Grü 1994].
29
2.2 Charge-Density Waves Investigated by Various Techniques
and Scientific Outstanding Questions
Thanks to advances in ultrafast lasers and pioneering work that developed the technique [Zew
1990], femtosecond time-resolved spectroscopy has been a new tool for studying the interplay,
transformation, reaction, and relaxation between lattice, charge, and spin degrees of freedom. The
interconnected order parameters, or the modulation of charge density is accompanied with the modulation
of the underlying lattice, presents a various degree of cooperativity that is crucial in the phenomena in
strongly correlated systems.
Numerous all-optical femtosecond time-resolved experiments have been performed on CDWs
[Dem 1999] [Dem 2002] [Shi 2007]. The Mihailovic group reported temperature-dependence of the
single-particle dynamics of electron-hole recombination, amplitude mode oscillations, and phase mode
damping time scale for the first time in an ultrafast reflectivity study on K0.3MoO3 [Dem 1999]. In the
relaxation of the femtosecond-laser-induced jump in reflectivity, they observed the two components
distinguished by their different time constants, and , in the dynamics (Fig. 2.2.1a) and attributed
them to phase mode damping and the recombination of single particles (SP), respectively. From the
temperature-dependence , they suggested the existence of a single-particle gap. Similar work was also
performed again on 1T-TaS2 and 2H-TaSe2 by the same group in 2002 [Dem 2002], and based on the
slower relaxation, shown in Fig. 2.1.1(b), when the excitation energy is less than the full gap, they
suggested a dynamically inhomogeneous intermediate state local precursor CDW segments to appear on
the femtosecond time scale. In 2007, Shimatake and coworkers reported similar finding in NbSe3, a
material exhibiting two independent CDW transitions that occur with different nesting conditions in k
space [Shi 2007].
Another femtosecond time-resolved technique is angle-resolved photoemission spectroscopy (tr-
ARPES) that ejects the electrons from the material via photoemission and allows the observation
30
Figure 2.2.1 Previous studies on 1T-TaS2. (a) The time evolution of normalized reflectivity measured at
different sample temperature, T = 45 and 110 K displayed in log scale to highlight the two time scale in
relaxation [Dem 1999]. (b) the temperature dependence of relaxation time of 1T-TaS2, plotted with result
taken upon warming in open symbols and cooling in solid symbols [Dem 2002]. (c) Dynamics of
Hubbard peak normalized intensity of 1T-TaS2 in Mott-insulator state [Per 2006]. (d) Shift of the
Hubbard peak that recovers in ps time scale [Per 2006].
of the density of states at different momenta, effectively mapping the band dispersion and Fermi surface.
Since the Fermi surface topology plays an important role in CDW formation, the direct observation of the
CDW bandgap and nesting condition provides valuable information. Using static ARPES, V. Brouet and
coworkers determined the Femi surface topology of CeTe3, shown in Fig. 4.1.3 (b), correlating the folded
part of the Fermi surface directly to the weak coupling between the lattice planes with poor conductivity,
which contributes to the 2D nature of the material [Bro 2004]. Utilizing tr-ARPES, Perfetti and
coworkers observed a 100 fs collapse and sub-ps recovery of the Hubbard band in the Mott-insulating
(a) (b)
(c) (d)
31
state of 1T-TaS2, shown in Fig. 2.2.1 (c). They also reported a long, 9.5ps recovery correlated to the
phonon relaxation [Per 2006]. In 2008, Schmitt and colleagues observed similar fast recovery of the
electronic part at the CDW bandgap and lingering lattice vibrations after an intense femtosecond
excitation [Sch 2008].
All these ultrafast optical pump-probe techniques focuses on the observation of the electronic part
of the CDW. These studies consistently present an outstanding puzzle regarding the identification of a
sub-ps partial recovery of electronic ordering being independent of the perceived underpinning
mechanism. This universality may be explained by the lattice being frozen in its modulated state on the
sub-picosecond time scale, but there has been no direct proof of this hypothesis. The sole atomically
sensitive study was reported by Eichberger and colleagues using an ultrafast electron diffraction
observation on 1T-TaS2 [Eic 2010]. However, this study only examined the dynamics of the CDW
without inducing a CDW phase transformation. Hence, the implications of the result are limited.
Together with the capability of direct observation of ultrafast structural evolution of a CDW and the low-
vibration cryogenic sample holder, we are poised to provide a complementary view to the mechanism of
CDW formation and to explore the energy landscape of CDW phase transitions.
32
CHAPTER 3
Ultrafast Electron Crystallography Techniques for
Studying the Low-Dimensional Material CeTe3
In this chapter, a brief introduction of electron diffraction theory is presented first to provide a
basic understanding of the phenomenon of diffraction. This is followed by the sample preparation and
characterization developed specifically for low-dimensional materials. During the development of the
sample preparation technique, we realized that having high-quality, well prepared samples is one of the
cornerstones for a successful experiment. Finally, in this chapter, we will briefly describe the experiment
setup of our UEC technique.
33
3.1 Diffraction Theory
Diffraction has been one of the most powerful techniques providing structural and compositional
information of materials. Since diffraction theory was developed originally using X-rays [Lau 1914] [Bra
1915], the majority of the crystallographic information we have about materials are obtained by X-rays.
However, Louis de Broglie proposed the wave-particle duality [Bro 1924] in his PhD thesis, which paved
the way for the development of electron diffraction [Dav 1927] [Tho 1928]. X-rays interact with the
electrons in a system, and it is the emission by these electrons of their own electromagnetic field, identical
to the incident X-rays, that creates the resultant field-to-field scattered wave. In comparison to X-rays,
electrons are scattered much more strongly, as they interact with the electromagnetic field of both
electrons and nuclei in the material, and these incident electrons are scattered directly by the target sample.
It is these attributes that allow electron diffraction to be used specifically for measurement of surfaces or
minute samples to determine the periodic structure of crystals, stacking faults, displacements, impurities,
et cetera. In the situation in which a large, high quality specimen is hard to come by or the material of
interest is of nanometer size, electron diffraction plays an important role in revealing structural
information.
3.1.1 Diffraction Condition
The de Broglie wavelength can be calculated by
(3.1.1)
where can be expressed as the kinetic energy and rest energy of electron via
(3.1.2)
that gives us
, (3.1.3)
34
Figure 3.1.1 Diffraction. (a) Elastic scattering from two planes consisting identical atoms. Vectors ki
and kf are the incident and scattered wave vectors. (b) Momentum transfer, s, being the vectorial change
of incident and scattered wave vector, while θsc is the angle between incident and scattered wave vectors.
where can be calculated from the acceleration voltage applied to the electron, is the mass of
electron, is the Planck's constant, and is the speed of light. For the typical 30 keV electron used in our
UEC experimental setup, the associated wavelength is = 7.0 pm. This shows that UEC is the ideal tool
for studying material on the nanometer scale.
Consider the incident wave of an electron beam striking two planes of identical atoms that
are separated by , and the final wave after electron scattering from the material, as shown in Figure
3.1.1(a). The diffraction intensity of the scattered wave on a screen in the far field is maximum if
these waves are constructively interfering. Namely, they exhibit a path difference of where is
an integer that denotes the order of diffraction. In a simple condition when , the path
difference of two adjacent waves is and the maximum diffraction intensity occurs when
(3.1.4)
which gives us the Bragg condition that relates the lattice distance , the scattering angle
, and the wavelength of the propagating wave .
To generalize the scattering process, we use the momentum transfer, where is the
wavevector of incident or scattered waves of the process, illustrated in Figure 3.1.1. With the and
(a) (b)
35
being the incident and scattered angles, respectively, the path difference of the same wave front scattered
from two adjacent scatterers is
, (3.1.4)
and the phase difference of the scattered waves is
(3.1.5)
which can be written in terms of the wavevectors
.1.
where . In the condition where the phase difference is , or the Laue condition, we expect
the maximum diffraction intensity when waves interfere constructively.
For a 30 keV electron, the scattering is essentially elastic, or . With
this condition, the momentum transfer , figure 3.1.1(b), can be expressed as
or
.1.7
Using the Laue condition, (3.1.7) can be reduced to the Bragg condition (3.1.4),
or .1.
3.1.2 Scattered Intensity
In a general scattering event, Figure 3.1.2(a), the scattering intensity recorded at the detector can
be expressed as the differential scattering cross section [AN 2001]
.1.9
36
Figure 3.1.2 Scattering process. (a) Generic schematic layout and notation of scattering process. (b) An
electromagnetic plan wave polarized with its electric field along the z axis forces an electric dipole at the
origin to oscillate [AN 2001].
where is the distance between scattering object and the detector, is the scattering cross section, is
the solid angle, is the scattered intensity recorded at the detector, is the strength of the incident
beam, and and are the radiated and incident electric field, respectively. In the case of X-ray
scattering, one can use the dipole approximation of the scattering of the electric field by an electron,
Figure 3.1.2(b), and the radiated over incident ratio can be derived as
.1.10
where accounts the polarization factor, is the incident wavevector, and is the fundamental
length scale, or Thomson radius:
.1.11
Therefore, the differential cross section for X-rays can be calculated as
.1.12
(a) (b)
37
Figure 3.1.3 X-ray scattering event from (a) an atom, (b) a molecule, and (c) and a crystal [AN 2001].
When considering X-ray scattering from an atom with Z electrons, one can consider that a
volume element at would contribute an amount of to the scattered field with a phase
factor of , where and being the number density. Hence the total scattering length of
the atom can be expressed as [AN 2001]
.1.1
where is the atomic form factor for the X-ray scattering.
Compared to X-ray scattering, which assumes the electron charge density is spherically
distributed, electron waves scatter coherently (Rayleigh scattering) from tightly bound electrons in the
atom as well. Therefore, to determine the electron scattering from an atom, one can calculate the electron
atomic form factor from the X-ray form factor using the Mott-Bethe formula [Kir 2010],
.1.14
where is the electron atomic form factor, is the Born radius, and Z is the atomic number of the
atom. When considering molecule or crystal scattering, however, the structure factor for the X-ray or
electron, after normalizing by the form factor, appears to be the same. Therefore the formalism of
scattering is interchangeable.
When considering a molecule, Figure 3.1.3(b), the scattering can be written as [AN 2001]
.1.14
(a) (b) (c)
38
where is the atomic form factor of the jth atom in the molecule, and a factor similar to that in
(3.1.13) is needed when calculating the intensity in absolute units.
Finally, for a crystal assembled by periodically spaced molecules, the scattering amplitude
factorizes into two terms,
.1.1
where the first term is the unit cell structure factor and the second one is the lattice sum.
For a crystal which is defined as a material that is periodic in space, we can describe the position
of every atom by , where specifies the origin of the unit cell and is the position of the atom
relative to that origin. The new aspect in (3.1.15) is the lattice sum. Each term in that sum is a complex
number which will contribute to most when all the phase terms satisfy
.1.1
This condition makes the lattice sum equal , the number of unit cells. The lattice vectors have the
form
.1.17
where are integers and are the basis vector that define the unit cell. A solution to
(3.1.16) can be found by introducing a reciprocal lattice spanned by basis vectors
.1.1
so that any lattice site in the reciprocal space can be written as
.1.19
where are integers. From (3.1.17) and (3.1.19), we can see
.1.20
which leads to the conclusion that
.1.21
39
This shows that is finite if and only if coincides with a reciprocal lattice vector . This is
known as the Laue condition. Hence the scattering from a crystal is confined to distinct points in
reciprocal space.
Consider a small crystal constructed with scatters spaced with dimensions
where are the numbers of unit cells in the respective direction. From (3.1.15), for a 3D crystal
we obtain
.1.22
.1.2
where each sum is a geometric series that can be rewritten as
.1.24
Therefore, the experimentally observable scattering intensity is
.1.2
which shows the scattering intensity is proportional to . Meanwhile, since zero diffraction intensity
occurs at , the width of the diffraction peak is proportional to . Hence, within
the penetration depth of our incident electron, we can obtain much stronger and sharper diffraction
patterns if we can include more scattering sites, or molecules, in the diffraction process,.
3.1.3 The Debye Waller Effect
At room temperature, the atoms in a crystal exhibit random thermal vibrations with an amplitude
on the order of m. Even at , atoms still perform oscillations. These atomic vibrations can
be tracked as an ensemble of lattice distances sampled through diffraction. Depending on the statistics of
40
the ensemble distribution, one can establish a relationship between the degree of vibrations and the
diffraction intensity, as discussed below.
The atom's position can be extended from the static position by a time-dependent displacement
in a form
.1.2
By replacing with (3.1.26) in time-averaged (3.1.14), we have
.1.27
.1.2
where is typically called the static structure factor. The exponential term in (3.1.28) can be
Taylor-expanded into
.1.29
Since and the geometrical average of over a sphere is , (3.1.29)
becomes
.1. 0
Therefore, the experimentally observed diffraction intensity can be expressed as
.1. 1
where the exponential part is commonly referred to as the Debye-Waller factor. Since potential energy
, we get
.1. 2
Therefore, (3.1.31) can be expressed in a temperature-dependent form
.1.
41
In our UEC experiment, the sample is excited with a laser and the lattice temperature should elevate after
optical excitation. Using (3.1.33), we can expect the relationship between the diffraction intensity before,
and after, the laser illumination on sample to be
.1. 4
The higher order reflection, or diffraction peak at larger values, show stronger effects due to changes in
lattice temperature.
42
3.2 CeTe3 Sample Preparation and Characterization
High quality CeTe3 crystals were grown by our collaborator, Christos D. Malliakas in Prof.
Kanatzidis group at Northwestern University. All manipulations were carried out under dry nitrogen
atmosphere in a Vacuum Atmospheres Dri-Lab glovebox. Cerium (~ 0.3 g, 99.9% pure, filling from
ingot, Chinese Rare Earth Information Center, Inner Mongolia, China) and tellurium (~ 8.8 g,
Plasmaterials, at 99.999% purity) were loaded into fused silica tubes of 12 mm diameter under inert
atmosphere. Then each tube was inserted into a 15 mm fused silica tube and a stainless steel mesh filter
was placed atop it. A small segment of fused silica tubing was used as a counterweight to keep the filter
in place during centrifugation. The tubes were flame sealed under vacuum (<10-4
torr) and heated to 900
oC at 24 hours for 1 day and cooled down to 650
oC in 5 days. Tubes were removed at 650
oC and
centrifuged to remove the Te flux. The morphology of the crystals is that of thin plates with a brown
(copper-like) color. After confirming the crystals were indeed high purity CeTe3 using EDS and X-ray,
the raw materials were sealed in a glass tube under vacuum then sent to our group for further sample
preparation.
In order to have sufficient electron to penetrate through the CeTe3, the sample has to get thin
down to below 100nm in thickness at an area that is at least the same size as our electron beam footprint,
typically ~30um. Following the guidance from Dr. Xudong Fan at Center for Advanced Microscopy, we
first waxed the single crystal CeTe3 bulk sample on to a stud, and then flattened it on one side with
diamond lapping film (1-5µm Diamond Lapping Film from Electron Microscopy Sciences, Cat. # 50350)
using water as lubricant. When one surface was flattened, the sample was glued (Vishay Micro-
Measurements M-bond 610) to a Transmission Electron Microscopy (TEM) slot grid (Ted Pella) to have
the other surface polished (Figure 3.2.1a). During the polishing, the sample was waxed on a stud and
pressure was applied by a custom grinder (Figure 3.2.1b). When the sample thickness was less than
-milling (Gatan 691, Figure 3.2.1c) process until
light penetrated the sample. During ion-milling process, we used 3 to 4 kV ionic Argon flow and incident
43
Figure 3.2.1 Equipments for sample preparation. (a) CeTe3 sample glued to the copper grid. (b) Custom
grinder for thinning the sample. (c) Gatan 691 Ion Milling Machine.
angle of less than 5 degree. The sample was rotating at 3 to 4 rpm when ion-milled, and the whole ion-
milling process took more than 10 hours in total before an edge was created on the sample surface.
The quality of the ion-milled sample was first checked with a TEM (JEOL 2200FS, 200kV).
The TEM image of CeTe3 sample (Figure 3.2.2a and b) showed a wide and thin area of material ideal for
UEC experiment. The TEM diffraction image (Figure 3.2.2c) showed clear satellite reflections (S1) along
the c* axis, which are circled in red, together with the much brighter main Bragg reflections (S0) with
square-symmetry, circled in blue. The relatively high intensity of satellite peaks confirmed the large and
high quality of the raw material made by our collaborator. Electron microprobe energy dispersive
spectroscopy (EDS) was also performed on several crystals of the compound and confirmed the 1:3 ratio
of the Cerium to Tellurium (Figure 3.2.2d).
The thickness was estimated to be ~50nm using Electron Energy Lost Spectra (EELS) of The
JEOL TEM. The estimated sample thickness was calculated using the integration of EEL spectrum [Lea,
1984] that extrapolated the ratio of thickness t over the characteristic mean free path λ in material from
the log ratio of the total number of electrons It in EELS and that of electrons having no energy lost I0
(Equation 3.2.1),
(a) (b) (c)
44
Figure 3.2.2 TEM observation on CeTe3. (a) Ion-milled opening at CeTe3 sample. (b) CeTe3 film at the
edge of the opening. The central dark spot is a burn mark on the CCD camera. (c) TEM diffraction image
of CeTe3. The satellite peaks appear on the two sides of the Bragg reflection along c* direction (circled in
red), while the main Bragg peaks, circled in blue, show square-symmetry along both a* and c* axes. (d)
EDS element analysis of CeTe3 sample showing ~1:3 ratio of Ce:Te. The Carbon trace was contributed
to the diamond lapping film used in the initial thinning of sample. The Copper trace was originated from
the cooper TEM grid the CeTe3 was glued on.
t
= ln
It
I0 (3.2.1).
The number of total electrons and zero-energy-lost electrons was linearly proportional to the intensity of
TEM transmission pictures taken without energy filter (Figure 3.2.3a) and that with energy filter that
blocked out energy-lost electrons (Figure 3.2.3b), respectively. Using these two pictures, the TEM
camera software produced the thickness map (Figure 3.2.3c) that intensity of each pixel is equal to ratio
of sample thickness t over the mean free path λ. The mean free path λ was calculated to be 92.58 ±
18.52nm, using the formulation derived by Malis, et al. [Mal 1988],
45
Figure 3.2.3 Thickness map on CeTe3. (a) TEM picture taken without energy filter. (b) TEM picture
taken with energy filter that blocks out energy-lost electrons. (c) Thickness map processed using (a) and
(b). The scale bar in (c) also applies to (a) and (b). (d) Typical EELS from CeTe3 material. (e)
Thickness profile of ion-milled CeTe3.
(3.2.2)
,
E0 is the energy of incident electron in keV, Em is the weighted average of energy lost of electron, and β is
the spectrum collection semiangle in mrad. From the EEL spectrum (Figure 3.2.3d) of our CeTe3
sample, Em is averaged from the 3 FWHM of the zero-lost peak as the lower limit to the end of spectrum,
100eV. This relativistic factor F was 0.0618 for 200keV incident electron, and β is 10mrad, according to
the manufacture of our TEM. By averaging the intensity of a 0.5um wide area in thickness map
(highlighted area in Figure 3.2.3c) and calculated λ, we obtained the thickness profile of our ion-milled
(c)
(d) (e)
46
CeTe3 sample respect to the distance from the edge of opening. From the method mentioned above, our
CeTe3 sample was estimated to be 20 - 80nm thick within 0.5µm from the edge of opening (Figure 3.2.3e),
which translated to 5.7 degree sample slope that is very close to the 5 degree incident angle of ionic
Argon during ion-milling process.
47
3.3 Experimental Setup
We perform ultrafast electron crystallography (UEC) in an ultrahigh vacuum chamber (Figure
3.3.1a) equipped with a custom goniometer to allow the experiment to be conducted in either reflection or
transmission geometry. In this technique, femtosecond photoelectron pulses are used to replace the
optical probe in the traditional all-optical pump-probe experiments to provide structural information on
the excited state following laser pulse excitation. The femtosecond electron pulse is generated at a silver
photocathode using 266 nm laser pulses produced by tripling the fundamental 800 nm 50 fs laser pulse,
which is also used as the optical pump to excite the sample. To minimize the temporal broadening of this
electron pulse due to space charge effects, a proximity-coupled cathode-lens assembly is employed
(Figure 3.3.1b). The electron pulse is accelerated to 30keV within a short distance of 4mm, collimated
first using a front aperture and allowed to pass through a magnetic lens running current at 320 ampere-
turns. The magnetic lens focuses the pulsed electron beam and the beam is further trimmed by a
replaceable exit aperture before intercepting the sample, which is typically 5cm away from the cathode.
The probe size can be controlled via adjusting the focusing strength of the magnetic lens or employing
different exit apertures, and ranges from 5 to 20 µm. The probe size is characterized in situ via a sharp
knife-edge technique. The temporal resolution of the UEC experiment is typically determined by the
condition of pump-probe overlap. In the reflection geometry, since the electron footprint is elongated
along the incidence direction by a factor of 1/sin θi , where θi is the incidence angle, the typical resolution
is around 1 ps due the velocity mismatch over the stretched probed region (~ 100 µm with incidence
angle of <5°). In the transmission geometry, the probe size is in the 10 µm range, so the temporal
resolution is ultimately controlled by the probe electron pulse, which is space-charge-limited. We have
characterized the space charge effects through imaging the real-space longitudinal electron pulse-length
by shadow-imaging technique [Tao 2012]. We establish a power-law growth of electron pulse-length due
to space charge effects, which can be used to chart the pulse-length of the electrons for a broad range of
electron counts per pulse, as shown in Figure 3.3.2a. For this experiment, we kept the electrons counts to
48
Figure 3.3.1 Experiment setup. (a) Layout of ultrafast electron crystallography apparatus. (b) Schematic
diagram of the proximity-coupled femtosecond electron gun.
be ~800 e- per pulse, the best estimate of the pulse-length is 390±110 fs (at FWHM).
To establish the pump-probe spatial and temporal overlaps prior working on the CeTe3 sample,
we use the reaction of a graphite sample that is mounted near the sample. First, we characterize the
pump laser profile by scanning the laser across the fine electron footprint on graphite surface and record
the opto-electrical response from the diffracted beam, from which we can determine Zero-Of-Time (ZOT),
or the time when pump and probe both arrive at the sample, to be within 500 fs [Rua 2009]. The timing
between the pump and probe pulses is adjusted using an optical delay stage in the optical path of the
pump laser. For this CeTe3 experiment, the transverse width (at FWHM) of the excitation laser is
determined to be 00 μm and is stretched along the beam direction to 0 μm considering the 4 °
incidence angle. Following the alignment, the CeTe3 sample is moved to the location of the pump-probe-
overlap, labeled on the screen of a CCD camera, and the overlap can be verified from the transient
response of on CeTe3.
At the same time, The transmission electron diffraction pattern of CeTe3 obtained using UEC
apparatus is shown in Figure 3.3.2b. Because of the disparity in S0 and S1 intensities, in order to record
the Bragg and satellite reflections simultaneously, UEC experiment is performed at an exposure time
(a) (b)
49
Figure 3.3.2 Experiment setup. (a)The electron pulse-length as a function of the number of electrons per
pulse employed. (b) Diffraction pattern of CeTe3 obtained from UEC setup.
where the main Bragg peak will reach 2/3 of the saturation level of our CCD camera, and frame-averaged
over 200 diffraction images to obtain an averaged time-resolved diffraction image at each time stance
with sufficient signal-to-noise level to quantify both S0 and S1 changes. Because of the smaller Ewald-
sphere at 30 keV (compared to TEM experiment), we slightly tilt the crystal along the a-axis to optimize
the intensity of the satellites along the (3,x) –stripe, as shown in Figure 3.3.2c, where satellites appear
most visibly at (3,±Q0) and (3,2±Q0) and are well separated from the Bragg reflections.
(a) (b)
(c)
50
CHAPTER 4
Structural Dynamics of Charge-Density Waves
CeTe3 is the first charge-density waves material our group study on. We are intrigued by its
unique uniaxial CDW formation that stands out among the already exotic charge-density waves material.
In this chapter, we first discuss the special property that gather much interests from other scientists. Then
we present the finding obtained from our experiment on CeTe3 and how we utilize its rare property to
provide information that other CDW material cannot.
51
4.1 Background on CeTe3
In the first experiment designed to probe the fluctuational dynamics of CDW, we choose to
investigate CeTe3 that belongs to the Rare Earth tritellurite system (RETe3), which is well regarded as a
model system to investigate 2D CDW formation, and can be quasi-continuously tuned by varying the RE
element. The novelty of this system is in its 2D non-correlated nature where all the steady-state
measurements seem to suggest it to be a rare case beyond 1D where the standard Peierls mechanism
actually applies [Bro 2004]. In the case of CeTe3, the weak electron correlation effect along with the
uniaxial CDW formation in a Te square lattice makes it ideal for studying symmetry breaking phase
transition in 2D.
In 1995, DiMasi and his colleagues first reported the CDW in RETe3 by transmission electron
microscopy [DiM 1995]. The CDW ground state has been studied with various techniques like APRES
[Bro 2004] [Shi 2005] [Gar 2007] [Bro 2008], variable temperature x-ray diffraction [Mal 2005] [Ru
2008], Raman scattering [Sac 2006] [Lav 2008], STM [Fan 2007], and susceptibility, heat capacity, and
electrical resistivity measurements [Ru 2006]. By substituting the rare earth element in RETe3 with
heavier one in the family, one can decrease the lattice parameters caused by Lanthanide contraction,
which is originated from the increasing screening of the core electrons with increasing number of 4f-
electrons [Ru 2008]. This effect leads to the increment of the wave function overlap, which increases the
electron density at the Fermi level , shown in Figure 4.1.1(a), that further dictates the chemical
pressure [Ru 2008]. With larger chemical pressure, for instance, the phase transition temperature and the
energy gap scale accordingly in RETe3 systems, as shown in Figure 4.1.1(b) and (c).
Comparing to the transition temperature calculated by BCS theory, which provides a fairly good
prediction for CDW properties (see section 2.1.4), the CDW transition temperature shows a significant
deviation. In the case of CeTe3 with a gap size of ~0.4eV, the BCS phase transition temperature
calculated using (2.1.73) is 2 00 , while it is predicted to be ~500K [Ru 2006]. This lower-
than-expected result can be rationalized by the fact that the Fermi surface is only partially gapped in the
52
Figure 4.1.1 Parameters of RETe3 family. (a) Energy density at Femi level as a function of the lattice
parameter of RETe3. (b) CDW gap size in various RETe3 material [Bro 2008]. (c) CDW phase transition
temperature in RETe3 where heavier RE element exhibit two CDW transition temperatures [Ru 2008].
case of the CDW and thermal fluctuations inhibit CDW formation [Ru 2008].
The lattice structure of CeTe3, shown in Figure 4.1.2(a), is weakly orthorhombic with space group
Cmcm, and consists of insulating corrugated double layers of CeTe sandwiched by the metallic planar
nets of Te making a CeTe3 slab [Mal 2005] [DiM 1995]. The slightly orthorhombic distorted Te net is
rotated 45o with respect to the CeTe double layer and has only half of the area, as shown by the structure
viewed along the b-axis in Figure 4.1.2(b). The stacking of the slabs is through van der Waals gaps along
the b-axis. The weak hybridization between the Te and CeTe layer causes a very large anisotropy with
the ratio between the b-axis and ac-plane conductivity ≥100. From magnetic susceptibility measurements,
Ru and his colleagues also indicate that the Ce is trivalent [Ru 2006].
(a) (b)
(c)
53
Figure 4.1.2 Parameters of CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal lattice.
The lattice constant 4. 4 2 .0 and 4.40 (b) The real-space model of corrugated
CeTe slab (gray/red) and Te net (red) viewed along the b-axis. The coupling from px and py orbital chains
from Te is also included. (c) An almost square Fermi surface calculated from a tight-binding model with
extended or reduced Brillouin zone, as well as two sets of 1D bands from coupling of px and py chains.
The Ce-donated electrons fill the Te p orbitals in the CeTe slab and partially fill those in the Te
planes [Kik 1998] [DiM 1995]. From tight-binding modeling, there are four bands that cross Ef, which
are derived from the 5px and 5py Te orbitals in the (a,c) planes, shown in Figure 4.1.2 (c) [Bro 2008].
Since these four bands form the valence band and are well isolated from others, the Te 5p orbitals define
the shape of the CeTe3 Fermi surface (Figure 4.1.2(c) and 4.1.3(a)). The calculated Fermi surface
correlates well with the results from APRES, shown in Figure 4.1.3(b) [Bro 2004].
Even at room temperature, the presence of a CDW can be observed, which makes the study of the
CDW in CeTe3 more convenient than in other materials. CeTe3's incommensurate CDW is predominately
along the c-axis of the underlying metallic planar square Te-nets at wave vector qcdw /7×2π/a where a =
4.4Å [DiM 1995]. From X-ray diffraction, the equilibrium A0 and Q0 are determined to be 0.15Å, and
0.28c*, respectively [Mal 2005]. From angle-resolved photoemission spectroscopy (ARPES), the CDW
(a) (b) (c)
54
Figure 4.1.3 Fermi surface of CeTe3. (a) Fermi surface of CeTe3, calculated from a tight-binding model,
consists the coupling from px (red), py (blue), and the limits of extended or reduced Brillouin zones [Ru
2008]. (b) Fermi surface of CeTe3 measured from APRES (solid black line) [Bro 2004].
gap is determined to be 0.4eV [Bro 2004]. At the same time, from optical studies on a series of RE
elements, the critical temperature (Tc) for CDW in CeTe3 to disappear is projected to reach above 500 K
[Ru 2006].
(a) (b)
55
4.2 Experiments on CeTe3
The electron-phonon interaction that leads to various charge-ordered systems is often
controversial because of the cooperative nature of the mechanism and the poor understanding of the
structural aspects of the transformation. A fast, sub-ps partial recovery of electronic ordering after optical
quenching has been consistently reported by earlier ultrafast spectroscopy studies [Dem 1999] [Sch 2008]
[Yus 2010] [Per 2006] [Kim 2009] [Roh 2011] [Hel 2010]. This quick recovery appeared across many
charge-density wave materials. This universality proved puzzling and sparked interest. One hypothesis
has been that the sub-ps partial recovery may be associated with the lattice being frozen in its modulated
state for a short time after optical excitation; however, there has been no direct observation. With UEC,
we first investigate this long-standing puzzle on a Peierls-distored 2D CDW in CeTe3.
From the CeTe3 experiment, we observe a two-step dynamics in suppression of the structural
order parameter of the 2D CDW of CeTe3 that decouples from its electronic counterpart following fs
optical quenching. By analyzing the Bragg reflection and its satellite peaks, we calculate the momentum-
dependent electron-phonon couplings of CeTe3 related to the interaction between the unidirectional CDW
collective modes, lattice, and the electronic subsystem. The time scales and the relative fluctuation
amplitude of these couplings allow us to determine the cooperativity between the electronic and structural
subsystem in hope of improving the understanding of the mechanism of charge-ordering.
4.2.1. CeTe3 Experimental Setup and Methods
The CDW of CeTe3 resides within the 2D square Te net and exhibits a uniaxial periodic lattice
distortion (PLD) at wave vector Q0=0.28c*, which can be monitored by the satellite diffraction peaks to
the sides of the main Bragg peaks, depicted in Figures 3.3.2(b) and 4.2.1. Following the axial assignment
in Figure 4.2.1(a), the Bragg peaks are indexed as (m,n) based on the reciprocal wave vector q=ma*+nc*,
while the satellites are labeled as ±Q0 next to their main peaks, Figure 4.1.1(b). Unlike 1T-TaS2, the
material presented in Chapter ? of this thesis, the unidirectional p-wave CDW in
56
Figure 4.2.1 Experiment result on CeTe3. (a) Crystal structure of CeTe3 with the corresponding
reciprocal lattice assignment with a=4.384Å, b=26.05Å, and c=4.403Å [Mal 2005]. Our femtosecond
(fs) electron pulse is directed along the b-axis, producing a transmission diffraction pattern, while the
fs laser pulses excite the sample area at 45o angle. (b) The top panel shows the 3D diffraction
intensity map, where the CDW satellites are located at a*± Q0 in the dashed region. The lower
panels display the temporal evolution of ultrafast electron crystallography patterns subtracted by the
equilibrium state pattern taken before fs laser excitation (t < 0) to showcase the induced changes.
The panels show both the ps sequences for Bragg reflections and fs-to-ps sequences in a scaled-up
view of the region near CDW satellites.
CeTe3breaks the underlying Te square lattice and displays weak electron correlation, which presents
unique advantages in deconvoluting the CDW-specific structure effects.
(a) (b)
57
The structural dynamics are investigated by an intense 0 fs infrared = 00 nm laser pulses at
1kHz to excite electrons across the CDW gap ranging from 1 to 7 mJ/cm2 in fluence. The anisotropic
electronic coupling, essential to the formation of the CDW and the quasi-1D Peierls distorted structure, is
present in the asymmetric response along the c-axis. At the same time, the nonspecific phonon
excitations from interaction with the hot electrons excited by laser pulses can be examined from the
orthogonal Bragg peaks as comparison. Because the satellite can be two or three orders of magnitude
weaker than the nearby Bragg peaks, we accumulate ~103 and ~10
6 electrons for the analysis of each
satellite and Bragg peak in order to achieve a high signal-to-noise ratio. The change, or the dynamics, of
these diffraction reflections (Figure 4.2.1(b), bottom panel) between the time before and after the 800 nm
pump laser provide a clear picture of the response of our CeTe3 sample.
4.2.2 Asymmetric Character of CeTe3
First, we focus on an orthogonal pair of Bragg reflection (-4,0) and (0,4) to investigate the
phononic response (Figure 4.1.2(a)) imposed on the 2D lattice by the hot carriers and CDW excitations.
The change in the intensity ratio of the Bragg peak (0,4) along the CDW axis is consistently larger than
the non-CDW-related one (-4,0), which indicates an elevated lattice fluctuation accompanying the melting
of charge-density waves. In terms of temporal response, the phononic signatures encoded in the (-4,0)
peak are delayed by ~1.5ps compared to the (0,4) one across all the fluences. This delayed response can
be identified as a signature of non-CDW-related electron-phonon coupling over the 2D lattice.
Furthermore, this asymmetry between the orthogonal Bragg peaks persists for more than 20 ps, indicating
that the two excited phonon manifolds, one coupled to the CDW and the other generated from 2D
electronic relaxations, are highly isolated from each other.
The satellite peaks, which represent the CDW collective state, show a clear two-step dynamics,
Figure 4.2.2(b), that is distinctively different than those from the Bragg peaks. Comparing the satellite
58
Figure 4.2.2 Dynamics of CeTe3. (a) The normalized Bragg peak intensity at q=-4a* and 4c* under three
different laser fluences: F=2.42, 4.62, and 7.30 mJ/cm2. The error bars are based on electron counting
statistics. (see Appendix A). (b) The normalized satellite intensity at qcdw=3a*+Q0 shows a nonscalable
two-step suppression.
response at different laser fluences (see Figure 4.2.3(a)) 80% of the maximum intensity suppression is
reached within 1ps at fluence F=2.42 mJ/cm2, while it takes 3 ps to complete the same task at F=7.30
mJ/cm2. This nonscalability underscores two distinctively different processes in the satellite dynamics.
The satellite peak suppression can be satisfactorily fitted by two independent exponential rise/decay
channels, shown by a dashed line for the case of F=7.30 mJ/cm2 in Figure 4.2.3(a). (The fitting protocol
is discussed in detail in Appendix B.) In Figure 4.2.3(a), the first channel, denoted as
, extracted from
the fits with three different fluences is presented, and all of them exhibit 350 fs suppression and
570 fs recovery time. This sub-ps time scale of
in response to laser pulses is very similar to
those reported in other ultrafast spectroscopy studies [Dem 1999] [Sch 2008] [Yus 2010] [Per 2006] [Kim
2009] [Roh 2011] [Hel 2010] [Tom 2009]. From the fitting result across a wide range of fluences, this
order parameter
saturates at Fc~3.8 mJ/cm2, as shown in the inset of Figure 4.2.3(b). In contrast, the
slower, ps dynamics, denoted as , exhibit a fluence-dependent suppression time, as well as a linear
relationship between the suppression amplitude and the applied fluence, as shown in the inset of Figure
(a) (b)
59
Figure 4.2.3 Dynamics of CeTe3. (a) Detailed view of satellite intensity change at early times showing a
two-step suppression, along with the two-component fits. The data from F=2.43 mJ/cm2 are multiplied by
3 in order to compare with data from F=7.30 mJ/cm2. The dashed curve shows the fitted result for F=7.30
mJ/cm2 data. The error bars are calculated based on the counting statistics. (b) The fast component of the
satellite suppression , showing a fast decay and recovery. The inset shows the amplitude of the fast
and slow
components extracted from fitting.
4.2.3(b). This fluence-dependent ps dynamics has not been reported previously and may represent the
characteristic features pertaining to the structural melting of a Peierls-distored 2D CDW.
4.2.3 Dynamics of Order Parameter of CDW in CeTe3
Due to the distinctive 1D and 2D lattice fluctuational features and the well isolated satellite
dynamics of CeTe3, we can quantitatively extract the phonon and CDW dynamics using the structure
factor previously derived by Guilani and Overhauser [Giu 1981].
4.2.1
where is the reciprocal lattice vector and is the electron scattering wve vector. and describe the
wave vector and the distortion amplitude of the CDW, respectively. is the Bessel function of the first
kind of order n, which provides the maximum intensity of 1st order satellite (n=1) and Bragg (n=0)
(a) (b)
60
reflections.
and are the collective mode attenuation factors induced by phase and amplitude
fluctuations ( and , respectively) within the CDW collective state:
and 4.2.2
where
and
4.2.
Finally, the Debye-Waller factor is accounted by the term
4.2.4
where being the atomic lattice fluctuation.
From this formulation, some observations can be made at the first glance. First, the satellites and
Bragg intensities are both influenced by the CDW order parameter because for a small , and
are anticorrelate with each other. Secondly, although the amplitude fluctuation plays no role in the
satellite suppression ( =1), it couples strongly to soft mode near [Sch 2008] [Yus 2008] [Lav 2008]
[Kus 2011] (Kohn anomaly, discussed in section 2.1.4) and directly contributes to the decay of Bragg
reflection along the c-axis. Thirdly, using the symmetry related to the hot-electon-relaxation-mediated
2D lattice fluctuation, we can deduce the uniaxial fluctuations from the anisotropy ratio
and, for example, in the insert of Figure 4.1.2(a).
Finally, the decrease of satellite intensity can either describe the actual suppression of the order parameter
term, or merely a reflection of temporal phase fluctuations term without reducing .
Utilizing the distinctive feature of CeTe3 allowing us to differentiate the non-CDW-related
contribution in the lattice response, we can calculate the CDW-related structural order parameter and
amplitude fluctuation from our experimental results following the Giulani-Overhauser formalism,
shown in Figure 4.2.4(a) and 4.2.4(b). To calculate , we have excluded the fast channel, which we
attribute to a phase-related decay induced by charge melting. This exclusion yields a clean result during 1
to 4 ps, shown in Figure 4.1.4(a), showing linear increment in suppression of the order parameter with
61
Figure 4.1.4 Order parameter of CeTe3 CDW. (a) the temporal evolution of the structural order
parameter . The reduction of represents symmetry recovery as described by the CDW potential
evolving from double well to single well (insert). (b) The CDW collective mode fluctuational variance
, deduced from anisotropy analysis. (c) CDW fluctuation amplitude order parameter
correlation plot.
laser fluence. The dynamical slowdown in the suppression of the structural order parameter can be
understood as inherent to a second-order phase transition that is driven by the softening of lattice potential
at (Kohn anomaly, discussed in section 2.1.4) [Cha 1973]. This phononic origin of the phase
transition can also be observed in the corresponding increment of fluctuational amplitude as the order
parameter is quenched, depicted in Figure 4.2.4(a) and 4.2.4(b). In Figure 4.2.4(c), a direct comparison
between the fluctuation and the order parameter shows the CDW melting following an arc trajectory
that starts from the equilibrium state with distortion 0.15 Å [Kim 2006]. With the fact that the
fluctuation amplitude reaches a similar value of 0.15 Å, it suggests the initial double-well potential is
quenched into a symmetric state, or the potential well literally flattened in the high-temperature CDW
state, depicted in the insert in Figure 4.2.4(c).
62
The origin of the ultrafast phase fluctuation might be attributed to the reduction of the long-range
coherence of the CDW collective state. Electronically induced fragmentation has been reported in
nanoparticles under surface plasmon resonance excitation without significantly transferring energy into
the lattice subsystem, as evidenced by a rapid nonthermal recovery in the structure factor following the
electronic recovery. The presence of this electronically induced fragmentation of the CDW is further
supported by the observation of topological defects in the optical reflectivity signals as the first step for
the recovery of the CDW in the electronic subsystem [Yus 2010].
Another novel aspect of 2D CDW melting, not identified by optical studies, is the momentary
stiffening of the lattice, which is the reason for the delay of the suppression of Bragg peak described
earlier, shown in Figure 4.2.2(a). This effect can be quantified by calculating the Debye-Waller factor on
(-4,0), as representative of the inherent lattice response to the fs heating of 2D electron gas. A narrowing,
or decreasing, of fluctuational variance occurs nearly instantaneously, as shown in the inset of
Figure 4.2.2(a). This narrowing can be translated into a stiffening in the mean atomic potential, which
has been observed in graphite [Ish 2008] under similar optical quenching. The mechanism for the
stiffening phenomena has been attributed to the inability of excited electrons to adiabatically follow the
lattice dynamics in low-dimensional systems, modeled by a density functional theory with nonadiabatic
implementation [Ish 2008]. As in graphite, this stiffening phenomenon lasts just over the hot electron
lifetime (~1ps) [Sch 2008]. After that, the 2D lattice might be heated first through optical phonon
emission at 0 and followed by the ensuing phonon cascades to reach thermalization, characterized by
the baseline rise of , shown in the insert of Figure 4.2.2(a), on an 7 ps ( ) time scale.
4.2.4 Cooperativity Between Electronic and Structural Subsystems
We have observed a sequence of events that can be traced to the interplay between the uniaxial
CDW-related soft modes, the lattice phonons, and the perturbed electronic subsystem. To quantify the
cooperativity, we use a phenomenological three-temperature mode (TTM) to capture the asynchronous
63
electronic and structural melting of the CDWs driven by the hot electrons and collective modes,
respectively. In our TTM framework [Mur 2009], the effective local temperatures and specific heats in
the electronic, CDW, and 2D lattice manifolds are labeled as and , where el, CDW, and ph,
respectively. We use the coupling equations
4.2.
to describe the energy exchange between these three manifolds, where is the coupling constant
between two manifolds and . Because the weak out-of-plane coupling between the Te planes, the
energy and charge diffusion along the z-axis can be ignored on the time scale considered here. Using the
time constants (el-CDW), (el-ph), and (ph-CDW) obtained in our experiments, we can establish the
constraints and solve the coupled differential equations iteratively. We also consider depth
inhomogeneity in the optical excitation (laser penetration depth nm) [Sac 2007]. We find this
simple three-temperature model adequately captures the key features of the space-time evolution of the
thermal energy flow in and out of the CDW manifolds. A more sophisticated three-temperature model
incorporating the proper z-axis diffusions and the hear capacities associated with each manifold has been
published [Tao 2013].
The overall concept of TTM is illustrated Figure 4.2.5. The photoinduced CDW dynamics is
initiated by the generation of hot carriers through above the CDW gap photoexcited by an intense laser
pulse, . The hot carrier generated by photon quickly equilibrate with the unexcited carriers at 100 fs
time scale. The optical energy stored in the electronic manifold decays into the lattice counterparts via
three coupling channels: the coupling the between hot carriers and 2D lattice phonons (el-ph), the hot
carriers and the CDW collective modes (el-CDW), and the 2D lattice phonons and the CDW collective
modes (ph-CDW). Using time constants (el-ph), (el-CDW), and (ph-CDW) of 7 ps, 3.3 ps, 40 ps,
respectively, and the formulism described above, the simulated dynamics follows well with the
experimental results, depicted in the lower panel of Figure 4.2.5. In that panel, the dashed line shows the
64
Figure 4.2.5 Conceptual framework of the three-temperature model (TTM). See text for notation.
TTM simulation at the surface (z = 0), while the solid line shows the simulation averaged across the
sample slab from 0 to 50 nm. These simulated results agrees well with the data points, the hollow points
in the Figure 4.2.5 insert.
The coarse-grained through-slab dynamics observed by the transmission ultrafast electron
crystallography is more than a factor of 2 less pronounced compared to the surface dynamics, which
65
provides relevant information when calculating critical fluence. The critical fluence for electronic
suppression, as determined from the departure from linearity in
, depicted in the insert of Figure
4.2.3(b), is reduced to 1.9 0.4 mJ/cm2, which is generally agreeing with the threshold (1-2 mJ/cm
2)
reported by ultrafast angle-resolved photoemission study of the isostructural TbTe3 [Sch 2008]. Using
this 1.9 0.4 mJ/cm2, we obtain the critical density u.c.v
u.c.v , where the reflectivity R=0.7 [Sac 2007] and u.c.v being the unit cell volume of 5×10-22
cm3 [Roh 2011]. In comparison, we also estimate the mean-field limit of the critical density based on the
CDW condensation energy (Eq. 2.1.70), where the CDW gap = 0.4eV [Bro 2004], the Femi energy
=3.25eV, and the ungapped density of states near Fermi energy =1.48 state/ev/(u.c.v) [Bro 2008].
The agreement between the mean-field calculated critical density, = 0.8eV/(u.c.v.), and our
experimental-extracted supports the idea that the fs partial structural order parameter response is
indeed correlated with the disruption of charge ordering.
4.2.5 Summary
We have established a two-step structural response to the optical quenching of the CDW, in
which the majority of structural suppression happens on the ps time scale, decoupled from the fs charge
melting. This observation is the direct proof that the periodically modulated ionic potential well has not
been significantly modified during charge melting, therefore the rapid recovery of the electronic order
parameter can be facilitated as proposed by Demsar and co-workers [Tom 2009]. We think that the
separation of structural and electronic order parameters is the result of the significant different in the
effective mass in these two subsystems, as well as the fact that the charge ordering is inherently coupled
to the valance electrons that are directly excited by the fs laser pulses. Once the electron temperature is
reduced to a threshold where a stable CDW condensate can exist, the coupling between the electronic and
ionic subsystems can reestablish. However, the cooling of the quasiparticle does not completely depend
on the CDW, as the 2D electron-electron and electron-phonon coupling would take place in the process at
66
the quasiparticle level. Therefore, the time scales of the first channel are directly related to the
quasiparticle dynamics, while it has little to do with the specific CDW mechanism. This is supported by
the apparent universality of the sub-ps recovery of charge ordering from monitoring the electronic
channel across a spectrum of different CDW systems. Therefore, important distinctions can be made
from the ionic frame through examining the ps structural response following the electronic perturbation of
the CDW. The noncooperative phononic signatures of CeTe3 illustrate a case of a fluctuation-dominated
phase transition and may very well represent the nonequilibrium dynamics for an entire class of
inherently Peierls-distorted electron-phonon system.
67
CHAPTER 5
Phase Transition of Charge-Density Waves
Phase diagram of 1T-TaS2 is filled with unique states, including Mott insulating, incommensurate
and commensurate CDW, and superconducting states. Previously these states can be accessed via thermal,
chemical-doping, or external pressure treatment. Utilizing optical excitation with different energy level,
we explore the energy landscape with ultrafast photo-doping to induce pathway that have never been
revealed, in hope to add more knowledge to the rich content of 1T-TaS2 phase transition. In this chapter,
the basic structural and charge-density waves phases of 1T-TaS2 are discussed first, then our experiment
result is presented with experimental detail at the end of chapter.
68
5.1 Crystal Structure and Charge-Density Wave of 1T-TaS2
1T-TaS2 belongs to the family of layered transition-metal dichalcogenides (TMD). TMD exhibits
simple crystal structures based on the stacking of three-atom thick layers, and 1T-TaS2 is the only TMD
material to develop the Mott insulating ground state in a commensurate charge-density wave (C-CDW)
[Sip 2008] [Faz 1979]. The middle layer of hexagonally arranged transition metal atoms is sandwiched
by two planes of hexagonally packed chalcogen atoms. These three-atoms-thick layers are bonded
together via van der Waals force along the c-axis, while the metallic sheets are predominately formed by
covalent interaction between each Ta atom [Wil 1975]. There are two ligand coordinations can be found
in TaS2: Trigonal-prismatic and trigonal-antiprismatic (distorted octahedral) coordination [Spi 1997].
While the prior case gives us the 2H-TaS2 and the octahedral structure builds the 1T-TaS2 polytype,
depicted in Fig. 5.1.1(a), it is possible to observe polymorphs that consists both types [Spi 1997]. Above
1100K, the 1T-TaS2 structure can be described by the point group 1 with lattice constants
3.3649 Å and 5.8971 Å [Spi 1997]. At room temperature, the 1T form can be retained by quenching
under sulphur environment if not reheated above 550 K [Wil 1975].
There are several CDW phase transitions reported on the pristine 1T-TaS2 across a wide range of
temperature [Ish 1991] [Wil 1975] [Spi 1997]. At temperature below
~225K, the so called Star-of-
Davis 13-atom clusters, builds up the entire C-CDW state. This polaron-like distortion is characterized
by the 6 Ta atoms in each of the two rings surrounding the central 13th atom moving inwards, depicted in
Fig. 5.1.1(b). This distortion couples significantly with the valance charge density redistribution within
the star. When warming up across 225K, the spatial inhomogenerities start to merge by breaking up the
C-CDW state into C-domains, first into a stripe phase where the CDW reconstructs into a near triclinic
local ordering (T-CDW), then into a near commensurate state with hexagonally ordered domains (NC-
CDW) above above
~280K [Tho 1994]. Scanning microscopy determined that locally within the C-
domains the CDW maintains commensuration in these textured phases, but the incommensurate regions
between C-domains grows with temperature, resulting in smaller C-domains [Tho 1994]. Above
69
Figure 5.1.1 Structure of 1T-TaS2. (a) The tantalum atom is located at center of six octahedrally
coordinated sulphur atoms. The lattice constant are 3.3649 Å and 5.8971 Å. [Spi 1997].
(b) The Star-of-David 13-atom cluster representing the unit cell of C-CDW in real space. The lattice
distortion within each star is coupled with a strong charge density redistribution. The angle between the
CDW vector and lattice vector is 13.9o.
Tc(IC)
~350K, the commensurate cells completely dissolve, and a new C-domain-free state arises with triple
incommensurate CDWs (IC-CDW). Finally, the N, CDW-free, phase would set in when all the distorted
Ta atoms move back to the symmetrical configuration at ~550K. A quick summary of different CDW
phases in pristine 1T-TaS2 is listed in Tab. 5.1.1.
The structural information of 1T-TaS2 were gained using X-ray, electron diffraction/microscopy,
and scanning tunneling microscopy (STM) [Bur 1991] [Van 1992] [Rem 1993] [Tho 1994]. Comparing
the results from these surface or bulk sensitive techniques, it is not surprising that the CDW formations
show little difference since the quasi 2D character of the 1T-TaS2 CDW is retained by the 3D interaction.
Fermi surface measurements [Cle 2007], calculations [Myr 1975], and observations of Kohn anomaly
[Wil 1974] strongly suggest a classical Peierls mechanism for the IC-CDW in 1T-TaS2. However, the
presence of the Mott state is still under discussion [Joh 2008] [Cle 2006] [Cle 2007].
(a) (b)
70
Phase Temp. on cooling
(K)
Temp. on warming
(K)
Angle (o) to a* on
cooling
Angle (o) to a* on
warming
C-CDW < 183 < 223 13.9 13.9
T-CDW - 223 < T < 280 - 13.0 - 12.3
NC-CDW 183 < T < 347 280 < T < 357 10.9 - 12.3 12.3 - 11.5
IC-CDW 347 < T < 543 357 < T < 543 0 0
N > 543 > 543 - -
Table 5.1.1 The different CDW phase in 1T-TaS2 and their manifestation in reciprocal space. The values
of transition temperature and angle associated with different CDW phases under the thermodynamic
conditions (cooling and warming) are taken from [Spi 1997] [Ish 1991].
The exact nature of these various CDW states has been a subject of considerable debate. First,
they are linked to a pseudogap (metallic) feature [Ang 2012] with polaronic conductivity [Dea 2011]. The
angle-resolved photoemission (ARPES) on pristine and doped TaS2 clearly identified coexistence of a
Mott-Hubbard gap and a nesting-driven CDW gap in different pockets within the Brillouin zone (Г and
M-K respectively) [Ang 2012]. The most recent crystallography studies indicated that the domain walls
(or solitons) are only a few atoms thick [Rit 2013], suggesting strong phase coherence between the
domains. It is also an open question whether the polaronic transport is mediated through soliton regions
[Sip 2008] or via a momentum-dependent mid-gap state created as part of a coherent interference effect in
deconstructing the Mott C-CDW state [Ang 2012] [Rit 2013]
71
5.2 Exploration of Meta-Stability and Hidden Phases of 1T-TaS2
Phase transitions are amongst the most fascinating properties of many-particle systems, and they
exhibit common features across very different scales ranging from exotic forms of nucleus [Guo 2011],
structured water [Sta 2014] , to galactic evolution [Sag 2009]. Whereas classical phase-change
phenomena have been well classified, exploration of phase transitions in quantum many-body systems is
an emerging field. Layered transition-metal oxide and chalcogenide compounds can exhibit exotic
quantum phases, including Mott insulator, superconductor, and spin or charge density wave states that
competitively emerge with subtle physical tunings, such as applying heat and doping. When multiple
electronic and structural orders are entangled, giant responses in the electronic and lattice degrees of
freedom can occur, seen in the resistivity change by several orders of magnitude in doping (or
temperature)-induced switching in manganite, magnetite, vanadium oxide, and several heavy fermion and
high-temperature superconductor compounds [Ima 1998]. Identifying the origins for the competitive or
cooperative emergence of various functional states responsive to doping, temperature, strain, or
electrostatic and magnetic fields is of vital importance for elucidating the basic physics and their
enormous technological potential. 1T-TaS2 is generally viewed as a prototype material for investigating
the emergence of quantum orders in correlated electron systems [Sip 2008] because, despite of its relative
simple composition, it exhibits an assortment of intriguing electronic phases, as reproduced in Fig.
5.1.2(a), including Mott insulating state, various textured charge-density wave (CDW) orders [Spi 1997],
as well as recently reported superconducting phase under chemical doping [Ang 2012] [Li 2012], and
pressure [Sip 2008] [Rit 2013].
Complex quantum phases emerge due to strong coupling and competition between electronic,
lattice, spin, orbital and other degrees of freedom. At equilibrium disentangling of the contributions of
these competing degrees of freedom is difficult; however, ultrafast pump-probe experiments can
temporally isolate the various degrees of freedom unmasking hidden states that have not been accessible
via conventional techniques. With UEC, we introduce high fidelity approach to revealing the ultrafast
72
Figure 5.2.1 Phase diagram and diffraction pattern of 1T-TaS2. (a) Generic phase diagram of 1T-TaS2
under various physical domains (temperature, doping x, or pressure P ) reconstructed based on reference
[Fau 2011] [Cav 2004] [Per 2006] The CDW phase evolution can be characterized by the changes in the
hexagonal CDW diffraction peaks at reciprocal vector Q: Amongst the phase transitions starting from the
C-CDW, the intensity of CDW and the angle of Q (with respect to G) are reduced suddenly at the phase
boundaries to approximately half and 0 (from 13.9) to the IC-CDW (upper-right corner). (b) The scale-
up view of the ultrafast electron diffraction pattern, showing the hexagonal diffraction patterns of C-CDW
(Q) surrounding the lattice Bragg peaks (G).
structural dynamics of complex quantum materials and contributes to the recent strong interest in
accessing various functional states in correlated materials using light [Sto 2014] [Fau 2011] [Ich 2011]
[Jon 2013]. We utilize optical excitation to exert influence on the electronic properties, similar to
chemical doping or applying pressure [Fau 2011] [Cav 2004] [Per 2006], but without uncontrolled effects
due to strain or disorder. Femtosecond (fs) pump-probe method(12) offers a unique possibility to drive
the system out of equilibrium by creating hot carriers while the lattice or long-range ordered states remain
less perturbed initially [Han 2012]. This selective excitation creates a crucial temporal window to
(a) (b)
73
disentangle the couplings that lead to various phase transitions. We compose a comprehensive study of
optically induced phase diagrams and answer several outstanding questions concerning thermal and
chemical effects induced by photo-excitation. The method of choice here is femtosecond electron
crystallography, with which we address the open issue of non-thermal effects in non-equilibrium photo-
induced phase transitions of 1T-TaS2. We elucidate the mechanics of coupling between macroscopic
electronic and lattice-ordered states, which enable an ultrafast phase transformation occurring well within
1 picosecond (ps). Moreover, we characterize ultrafast optical doping-induced transition pathways
through a succession of meta-stable phases and establish the first temperature-optical doping phase
diagram to delineate the temperature and interaction-driven phase behavior of complex materials.
We study the stable and transitory many-body states of 1T-TaS2 by fs optical doping using two
different laser wavelengths, =800 and 2500 nm, with photon energies E of 1.55 and 0.5 eV respectively.
The initial state used in the experiments is the electronic crystal situated deep inside the Mott insulating
phase at 150K. Since 1T-TaS2 has an insulating gap Eg~0.3-0.4eV [Ang 2012] in this phase, the two
pump energies that we used deliver distinctly different excess energy = E- Eg for driving the initial
electronic temperature Te. Both pump energies produce photo-generated hot carriers that drive a quantum
transition of the Mott state on the timescale of electron thermalization, as revealed in recent ultrafast
spectroscopy experiments [Per 2006] [Hel 2010]. However, for the 800nm pump experiment, a phase
transition into a stable metallic regime cannot be established below the fluence ~ 2 mJ/cm2, which is near
the thermal threshold indicating a typical thermally driven behavior. In contrast, a pioneering ultrafast
electron diffraction experiment [Eic 2010] initiated in the NC-CDW phase indicated a strong
cooperativity between the CDW amplitude suppression and the electronic gap closing but without
evidence of direct coupling to the domain dynamics. To be complete, we comprehensively investigate
phase transitions into all of the CDW phases, studying both the temperature-driven dynamics typical of
the high energy pump pulse near TC and the non-thermal behavior evidenced by the mid-infrared pump
74
pulse at low temperatures. The temperature-optical-doping phase behavior is characterized by tuning the
electron temperature Te, optical doping x, and crystal base temperature TB for both pulse energies.
We prepared thin flakes of TaS2 from a 1T-type bulk single crystal by the Scotch tape method
widely used in exfoliating 2D materials. (See section 5.3.1 for sample preparation and section 5.3.2 for
experimental details). The exfoliated, free-standing sample flakes were transferred onto a TEM grid
docked inside an ultrahigh vacuum ultrafast electron diffraction chamber [Rua 2009]. For our
experiments, we selected electron-transparent flakes 30-50 nm in thickness estimated by zero-loss
electron energy loss spectroscopy (EELS) thickness map, as described in section 3.2. The probe electron
beam density is adjusted to balance between resolution and sensitivity. For mapping the phase diagram,
~10,000 electron per pulse is used to gain efficiency, whereas for studying the dynamics ~ 500 electron
per pulse is delivered to reach ~ 300 fs resolution (FWHM) at 30 keV [Rua 2009]. Our pump laser is
spectrally tuned using an optical parametric amplifier, delivering 50 fs mid-to-far infrared pulses, which
are expanded to 400 µm at FWHM so the selected sample flakes ≤ 0 µm wide) can be excited
homogeneously. The high quality of the diffraction patterns obtained using our fs electron
crystallography system can be seen in Fig. 5.2.1(b), as judged from the well separated hexagonal arrays of
CDW peaks (Q) around the atomic lattice vectors (G) in reciprocal space. In the C-CDW state, the three-
fold-symmetric Q1(C)
=1/13(3G1-G3) peak is clearly distinguished from that of the IC-CDW where
Qi(IC)
~0.282Gi, by the orientation angle of the respective Q with respect to lattice G ( in C-CDW and
IC-CDW is 13.9 and 0 respectively).
We use the orientation angle , depicted in Fig. insert of 5.2.1(a), and the CDW-induced lattice
distortion amplitude A to quantify the ordering of various textured CDW states. As well characterized in
the steady state crystallography studies, described in section 5.1 and re-plotted in Fig. 5.2.2, is
temperature-dependent between TC(T)
and TC(IC)
and takes on sharp jumps as the phase transitions
transform into soliton states (T or NC). Correspondingly A, monitored as a function of the scattering
intensity at Q [ A ICDW(Q)1/2
] [Han 2012], is strongly coupled to in thermal equilibrium, exhibiting
75
Figure 5.2.2 Transitions of 1T-TaS2 upon heating, showing complementary changes in the resistivity and
the CDW orientation angle extracted based on electron diffraction (ED) [Ish 1991].
correlated changes at the various critical temperatures. Since the 13-atom Star-of-David reconstructed in
the C-CDW domains leaves only 1 electron in the uppermost reconstructed band at half-filling, it exhibits
the Mott-Hubbard transition and the polaronic distortion of the C-clusters associated with filling of the
lower Hubbard band (LHB). Optical doping leads to tuning away from half filling, leading to changes in
phase behavior as characterized below.
We studied the laser pump fluence(F)-dependent conversion of the Mott insulator C-CDW state
into various phases at TB=150K. We found that at times greater than 20ps after the initial pump pulse, ,
shown in Fig. 5.2.3, the sample has reached a quasi-equilibrium phase, so we chose the time delays of (-
10ps) and (+20ps) as the reference states before and after the laser pump. The laser pump repetition rate
of 1kHz corresponds to a much longer timescale. We monitored the relative change of the CDW peak
intensity as well as rotational angle , and used them
to map out the F-dependent phase behavior. First we describe the responses to the 800nm pump laser
pulse. At fluence F=1.8mJ/cm2, Q rotates from 13.9
o to 13.4
o, which means the sample goes from C to T-
76
Figure 5.2.3 Typical dynamics of Bragg and satellite (CDW) peaks of 1T-TaS2. Dynamics of each
components have been normalized and scaled for comparison.
phase. At F=3.6mJ/cm2, Q further rotates from 13.4
o to 12.9
o, going from T to NC-phase. Between
F=3.6mJ/cm2 and F=6.0mJ/cm
2, it is in the NC* state (see discussion below) and above F=6mJ/cm
2, IC
state is the final state. Intriguingly, this 1.8 mJ/cm2 threshold for entering the T-phase, evidenced by
CDW gap reducing to the NC level and the formation of a mid-gap feature, is also found to be the
threshold for melting the Mott state in the latest ultrafast photoemission study [Hel 2010]. Below this
threshold, the quenching (partial) of the Mott gap is still clearly visible although the effect is reversed
within 680 fs [Per 2006], suggesting the existence of a structure-bottleneck for stabilizing the new phase.
At this threshold, the electronic temperature reaches 3000 K initially [Hel 2010]. For the 800nm pump
pulse, a calculation of the energy transferred to the lattice in the final state indicates the transitions above
77
Figure 5.2.4 Comparison between the thermal and optically induced changes of over absorbed energy
density (see section 5.3.4 for calculation). The temperature of 1T-TaS2 is at 150K initially.
are consistent with the transition temperatures found by conventional means, confirming that at this pump
energy the behavior can be described using thermodynamic reasoning.
However for 2500nm wavelength pump we find that the optically driven phase transitions in 1T-
TaS2 are nonthermal. To demonstrate this, we map out the fluence-dependent phase behavior for the mid-
infrared pulse and compare it to the phase behavior described above for the 800nm pump. To make this
comparison, we convert fluence-dependent maps at the two wavelengths into absorbed energy-density
maps, seen in Fig. 5.2.4, which clearly shows that the critical energy densities for inducing various quasi-
equilibrium phases are very different for the two laser energies. In Fig. 5.2.4, the black curve is the
reference curve of equilibrium measurement shown in Fig. 5.2.2 in red solid dots, but only the horizontal
axis is converted into absorbed enthalpy (H) based on integration of specific heat (see section 5.3.4 for
calculation). This result shows that energy density required for phase transition with 800nm photons is
slightly higher than the thermodynamic value, while that with 2500nm photons is much lower.
78
Figure 5.2.5 The optically induced evolution of CDW states characterized by CDW suppression (in ratio,
based on unperturbed CDW intensity) and orientation angle at various absorbed photon density for two
different pumps: 800 and 2500 nm.
To understand the effects of photo-doping, we convert the enthalpy change into carrier density
, assuming that each absorbed photon generates an electron and a hole). Using photo-
doping as the axis, the two curves for the 800nm and 2500nm pump pulses now agree very well, seen in
Fig. 5.2.5 as black points. The result shows that to induce the same state with different wavelength
pumps, it is necessary to induce the same density of charge carriers rather than to provide the same
enthalpy change. This strongly suggests that the system is driven by charge carrier doping, rather than
through thermal pathways. Moreover, photo-doping has similar effects as those produced via chemical or
electrostatic doping, as the optical doping effect relies on electron/hole asymmetry, common in TMD and
79
many other correlated electron crystals [Ima 1998]. Upon pumping electrons into the conduction band, a
spontaneous charge separation occurs due to the more restricted dynamics of the holes left in the LHB,
effectively shifting the chemical potential, hence the coupling near EF, thus creating a transient doping
effect [Sto 2014] [Per 2006] [Dea 2011]. We show here that while the typical electron-hole
recombination timescale is on the ps timescale at low doping, once a new metastable state is transiently
entered, the energetics of the interaction potential change fundamentally, leading to a lock-in to a new
charge density and a stability that is beyond the first 100 ps [Sto 2014].
We now compare the critical optical doping level to the doping carrier-density induced by
applying electrostatic fields or chemical doping in other TMD materials, which commonly develop CDW
states at or close to half-filling. A large capacitance sustained by an ionic liquid electrical double layer
(EDL) has been used to deliver a 2D carrier density n2D up to 1.5×1014
cm-2
by electrostatic doping to
vary the band filling in MoS2 [Ye 2012], and a field-doping-induced superconducting (SC) dome was
established with a peak at n2D = 1.5×1014
cm-2
. Optical doping in 1T-TaS2 can easily reach this level, and
the n2D calculated from the critical doping at the C-to-T and NC-to-NC* boundaries are 0.5×1014
and
1.3×1014
cm-2
respectively, matching the critical values found in MoS2 very well. The corresponding
doping level is x=0.05 and 0.12, which is often sufficient to induce new phases by chemical doping. To
our knowledge no one has been able to gate-dope 1T-TaS2 with EDL because of its high intrinsic carrier
concentrations. The optical doping method established here offers an alternative route to access higher
doping concentrations than chemical doping, and to explore various doping-induced novel quantum
many-body states without substantially deforming the lattice.
We have explored the experimental analysis of photo-doping-induced phases in various
temperature regimes from which we extract a first temperature-carrier density phase diagram for 1T-TaS2
as depicted in Fig. 5.2.6. Comparing to Fig 5.2.6 and Fig 5.2.1(a), the temperature-photo-doping phase
diagram is strikingly similar to that found for the generic chemical doping (or pressure) phase diagram
presented. At low T the critical density (or pressure) is insensitive to the temperature changes of the
80
Figure 5.2.6 The temperature – photon-density phase diagram of 1T-TaS2.
sample, and the phase transitions may be characterized as interaction-driven where new dominant phases
emerge from the change in the free energy of different states resulting from chemical potential shift.
Conversely, in the regime with low doping (or pressure), the phase transition is mostly temperature-driven.
Based on this phase diagram, the thermal-like emergence of metallic state investigated using the 800 nm
pump in the previous ultrafast photoemission studies of 1T-TaS2 [Per 2006] [Hel 2010] is expected as the
experiment was conducted in the temperature-driven region near TC(T)
and limited to the boundary of
insulator-metal transition. Similar conclusions have been drawn from studies of other correlated
electronic crystals[Jon 2013] [Bau 2007], which are expected to have similar generic forms in their phase
81
Figure 5.2.7 The dynamics of CDW state transformations inspected via the rotation of CDW wave vector
Q away from C-CDW and the suppression of ICDW(t) [in ratio based on the ICDW(-10 ps)]. The solid lines
are drawn based on fitting the stair-case rises using a Gauss Error function.
diagram. Limited by our current cooling capability ≥ 20K) , we were unable to inspect the emergence of
SC (TC = 8K at optimal doping) within the T and NC states. However, we discover that a hidden state not
observed in the thermodynamic phase diagram, termed here as the NC* state. As indicated in Fig. 5.2.5,
the NC* can be characterized as a precursor to the domain proliferation in the NC-to-IC transition, or a
self-organized subdivision of domains before complete dissolution of commensurate cells. The
intermediate domain structure between the NC and IC states is meta-stable in the dynamical regime,
82
evidenced in the continuous transition, Fig. 5.2.5, but absent at the thermodynamic timescales of the
transition from NC to IC state, Fig 5.2.2.
A remarkable capability of the ultrafast crystallography data is to study the nonequilibrium
transition state pathways evident in Fig. 5.2.7. The dynamical transformations are explored using 2500
nm photons and TB=150K, in a region predominantly driven by doping effects. We drive the system with
three selected photon densities, targeting the ‘final states’ of T, NC, and NC*. This near-gap mid-infrared
pump ensures a small excess energy or thermal imprint on the dynamics after reaching the quasi-
equilibrium state. The results of satellite peaks dynamics are depicted in Fig. 5.2.7, where the upper panel
shows the evolution in , and the lower panel depicts the corresponding changes in A (through the
ICDW). Intriguingly these transient features are highly organized and exhibit unexpected sharp jumps in
temporal steps as short as 200 fs (2 in error function fit, resolution limited). All of these sharp
transitions are followed by a plateau region, defining the characteristic values and , which can be
traced to the quasi-equilibrium phase map depicted in Fig. 5.2.5. for the various CDW states; however the
emergences of these two order parameters are not synchronized. Quite persistently, the shift of CDW
amplitude leads the change of angle in time, implying suppression of the local charge density amplitude
within the C-CDW domains is a precursor for setting off the domain dynamics and deconstruction (as
described in Fig. 5.2.8). Moreover the emergence of a higher-doped phase cannot proceed without the
lower-doped one being established first, leading to a succession of steps in the dynamics. The only
exception may be for the occurrence of T, whose domain structure is not substantiated and the first clear
jump following the pump is the NC structure (Fig. 5.2.7, upper panel), whereas according the amplitude
suppression (Fig. 5.2.8, lower panel) a well-defined shift into that characteristic amplitude similar to the
quasi-equilibrium T state can still be identified. It is important to note that these transformations occur
largely within the typical electron-lattice coupling time of the system (several ps), so the evolution may
be considered to be within a closed system with essentially no change in temperature. Furthermore, in
contrast to the quasi-equilibrium map (Fig. 5.2.5.) the emergence of the NC* state at is very
83
Figure 5.2.8 Cartoon depiction of the dynamical evolution CDW states in a zig-zag pathway over the free
energy contour defined by the changes in and A2 based on the dynamics extracted from (A). A is scaled
to 0.15Å at C-CDW state based on reference [Spi 1997].
distinct and leads to another sharp jump into the quasi-IC state (IC* in Figs. 5.2.7 and 5.2.8.), which is
meta-stable at nearly continuous all the way to canonical IC state ( 13.9°) depending on the
strength of excitation. All the transformations cease to evolve after 4ps, which we assign as the timescale
for carrier recombination [Sto 2014].
The observed phase conversions, namely the presence of a threshold and an incubation period
inversely proportional to the pump flux, indicates that the phenomena we described are in the class of
photoinduced phase transitions (PIPT) [Nas 2004]. A simplified 1D PIPT model introduces a long-range
coupling term in an equation of state to treat a photo-doping-controlled inter-conversion rate describing
the transition between two states with these major features [Oga 2000]. However, to capture the first-
order-like sharp transitions in many PIPT systems, e.g. manganites [Ich 2011]] [Tak 2005] and
organometallic spin-crossover complexes [Oga 2000] [Lor 2009], one would require a 2D simulation
84
treating inhomogeneous spatial variations seeded by photo-excitations [Nas 2004] [Oga 2000]. Such a
percolative pathway necessarily engenders time-consuming steps with difficulty in accounting for the
observed femtosecond scale switching, given the typical NC domain size of 73 Å [Tho 1994] and the
large size of the crystal. We speculate that PIPT might be better described by a highly self-organized,
nondiffusive process involving collective polaronic waves or mesoscopic quantum correlations to access
different topologically distinct states in the femtosecond timescale, as seen in Fig. 5.2.8. However more
theoretical analysis and experiment is required.
We expect this 1T-TaS2 study will have significant ramifications in several areas of research.
First, the presented methodology opens up a new avenue to survey the complex energy landscape and
provides a new perspective on doping-induced phase diagrams, avoiding the difficulty of electrostatic
gating or confounding effects due to defects and/or disorder when doping by intercalation or substitution.
Second, the speed and degree of photodoping substantially exceeds that achievable by the conventional
methods, creating the opportunities to generate new phases, as evidenced in recent studies [Sto 2014] [Ich
2011]. Third, observation of robust non-thermal switching at meso-scales and at ultrafast times provides a
platform for new applications of correlated crystals for designing high-speed low-energy consumption
nano-photonics and electronics devices.
I would like to thank for the time and sweat Faran Zhou spent on this 1T-TaS2 phase diagram
project. Without his delicate hands in sample preparation, his experimental skill in instrumentation, and
his persistent work in data analysis, this project would not exist.
85
5.3 Additional Materials for 1T-TaS2 experiment
5.3.1. Sample Preparation
The high quality single crystal 1T-TaS2 are synthesized by our collaborator Dr. Christos
Malliakas in Prof. Kanatzidis' group at Northwestern University. The method of synthesis is described by
Chris in the following paragraph.
Single crystals of 1T form of TaS2 were grown by the chemical vapor transport technique. Pure
elements of Ta (1.426 g) and S (0.518 g) were loaded with a 1:2.05 ratio into a fused silica tube (9 mm in
diameter and around 24 cm in length) together with a small amount of I2 (0.068 g). The tube was flame
sealed under vacuum (< 10-4
torr) and placed in a dual zone furnace with a hot zone at 950 ºC and a cold
zone at 900 ºC. The temperature was ramped up in 1 day and the tube was soaked for 2 days at the target
temperature. After 1 day of cooling time, single crystals of different sizes were formed on the cold side of
the tube [End 2000].
After receiving the 1T-TaS2 bulk material, which was sealed in ~10-3
torr vacuum to minimize
oxidation, we cut a thin piece from the bulk sample with razor blade to obtain the initial piece, pictured in
Fig. 5.3.1(a), for mechanical peeling [Nov 2005]. The initial piece of 1T-TaS2 is sandwiched between
two scotch tape or wafer dicing tape, then cleaved when the two tapes are peeled apart. Since 1T-TaS2 is
a 2D material, this exfoliating technique yields flat surface cleaved along the lattice plane, shown in Fig.
5.3.1.(b). With multiple times of cleaving using scotch tape, the 1T-TaS2 can be thinned down to below
30nm in thickness. The samples can be prescreened in thickness by monitoring the transparency under
optical microscope with light going through the sample stage, shown in Fig. 5.3.1 (c) and (d). The sample
thickness can be measured by AFM once the material is transferred to silicon surface or by EELS
function of a TEM, described in section 3.2, if the sample is transferred to a TEM grid.
To transfer those 1T-TaS2 pieces on tape onto a silicon surface, we put a drop of acetone on the
cleaned silicon chip, then cover the silicon with the scotch tape while 1T-TaS2 samples facing the
86
Figure 5.3.1 Optical images of 1T-TaS2. (a) Optical picture of cleaved 1T-TaS2 from bulk as a starting
piece for exfoliating. (b) 1T-TaS2 on scotch tape after exfoliated once. (c) Optical image of peeled 1T-
TaS2 sample taken with light coming from below the sample stage. (d) 1T-TaS2 samples after multiple
"peeling".
silicon. The tape is pressed against the silicon by hand for several minutes to ensure high transfer rate.
The acetone would dissolve the glue on tape and release the 1T-TaS2 pieces from tape to silicon, shown in
Figure 5.3.2 (a). The samples on silicon are perfect for thickness measurement, as well as the electrical
measurement in the future if implemented.
To transfer those 1T-TaS2 pieces from scotch tape to TEM grid, we first suspend the 1T-TaS2 in
acetone by sonicating the scotch tape in acetone for a few minutes. Then the acetone solution is dropped
onto a TEM grid and the 1T-TaS2 would be suspended on the grid after acetone is dried up, shown in Fig.
5.3.2(b). The thickness of sample on a TEM grid is measured based on the EELS thickness map method,
(a) (b)
(c) (d)
87
Figure 5.3.2 Optical images of 1T-TaS2 samples. (a) Thin 1T-TaS2 samples on silicon surface. (b) 1T-
TaS2 samples on TEM grid ready for UEC experiment.
described in section 3.2.
5.3.2. Experimental Details
To study the phase transition of 1T-TaS2, our sample cryogenic sample holder is upgraded to
achieve low vibration while maintaining low temperature capability. By suspending the cryogenic motor
that creates vibration when cycling the helium into the cooling column with an aluminum frame secured
to walls and floor, we isolate the sample column from the motor and minimize the vibration transmitting
to the sample holder. We are able to minimize the vibration level below 5um or our detection limit while
(a)
(b)
88
maintaining the cooling capability of 20 K. The sample holder temperature is measured with 0.01K
precision. The TEM grid containing 1T-TaS2 for experiment is clamped into a cooper countersink on the
sample holder. The sample temperature is calibrated to be within < 1K of the measured reading using the
phase transition temperature of VO2 [Tao 2012]. The UEC pump-probe setup is identical as those used
for CeTe3 experiment, described in section 3.3, except the addition of 2500nm laser as optical excitation.
The 2500nm laser is generated by TOPAS from Spectral Physics (described in section 6.3), driven by a
45 fs, 800nm amplified laser system (Spectra Physics, Ti: Sapphire, Regenerative Amplification). In the
1T-TaS2 experiment, the size of pump beam of different wavelength is adjusted by varying the position of
a focusing lens in the path, and is characterized by the knife-edge method in situ. The pump size is set at
~400um in FWHM, which is more than 10 times larger than the 1T-TaS2 sample size to ensure the
homogeneous laser fluence across the sample. For the dynamics of CDW state transformation, we use the
~500 e- per pulse as electron probe, which is estimated of pulse-length of 300fs in FWHM that defines
the shortest response time in our experiment [Tao 2012].
5.3.3 Data Analysis for 1T-TaS2 Experiment
We focus the data analysis on determining the satellite peak intensity and the orientation angle
between the CDW wave-vector (Q) and the lattice vector (G) (see Fig. 5.3.3). To obtain the satellite peak
profile, we employ line intensity scans along the direction perpendicular to CDW vector crossing the
CDW peaks. The width of the line scan is set as twice of the FWHM of the CDW peaks so it covers most
of the individual peak but not the neighboring peaks. To determine the peak location and intensity, we
use Gaussian function to fir the peaks with second order polynomial background underneath the
Gaussians. Same fitting methods is also used for Bragg peak analysis. The angle is determined after
the Q and G vectors are calculated.
89
Fig. 5.3.3 Diffraction pattern of 1T-TaS2. (a) Diffraction pattern of 1T-TaS2 in the NC-CDW state taken
at room temperature. The image is in logarithmic scale to make CDW peaks more visible. (b) Scale-up
view of the diffraction pattern from the square region in (a), showing clear hexagonally distributed first-
order CDW satellite peaks around the central lattice Bragg peaks. Second-order CDW satellite peaks are
also visible. (c-e) Time-dependent diffraction images from a single Bragg peak region at different time
delays: -1ps, +1ps, +3ps respectively. The solid line connects neighboring Bragg peaks, representing the
direction of the lattice vector G. The dashed line connects neighboring CDW peaks, representing the
direction of the CDW vector Q. ϕ represents the angle between CDW and Bragg vectors. In (e), CDW
vector rotates fully into the lattice vector direction, indicating that the NC-CDW is transformed to IC-
CDW by 3 ps.
5.3.4. Calculation of Energy and Photon Density
We determine the absorbed energy density using the following formula:
. .1
Q G
(a) (b)
(c) (d) (e)
90
Figure 5.3.4 The determination of CDW phase boundaries based on presence of a step or a slope change.
where is the pump fluence on sample surface, R is the reflectivity and is the penetration depth of each
wavelength laser calculated from the optical constant measurements in literature [Bea 1975], and is the
sample thickness.
From the literature, the reflectivity for 800nm of 1T-TaS2 is 0.45 while it is 0.58 in the case of
2500nm laser. The penetration depth is calculated to be 30nm for the 800nm at both room temperature
and 150K. Given the phase diagram is determined at a longer time, +20ps), at which the carrier density is
expected to equilibrate between different layers over the range of t, we use the thickness t as the
denominator in Eqn. 5.3.1. Since for 2500nm laser, however, the calculated penetration depth is 100nm
91
at room temperature and 130nm at 150K, which are significantly larger than the 40nm sample thickness,
we use in the denominator in Eqn 5.3.1.
For calculating the energy density absorbed by the sample required to induce thermodynamic
phase transition from our base temperature, 150K, we integrate the hear capacity and latent heat of
1T-TaS2 in the temperature range we work with. Based on the reference [Suz 1985], we calculate the
energy density needed to induce thermodynamics phase change using
. .2
5.3.5 Constructing Phase Diagram
The temperature-photon-density phase diagram, Fig. 5.2.6, is constructed based on the critical
density of the emergence of each CDW state via monitoring the CDW wave vector Q and the intensity
I(Q). The absorbed photon density is converted from absorbed energy density, Eqn. 5.3.1., via
. .
where is the photon energy. We characterize the boundary between different phases by a step in the
angle ϕ of Q relative to G, or by the slope change of ϕ , as exemplified as those blue circles in Fig.
5.3.4.
92
CHAPTER 6
Dynamics of Nanoscale Water on Surface
The property of water has been great interests to scientists due to its ubiquitousness in our lives.
The prospect of elucidating some mystery on the most intriguing molecule is a dream project for many.
However, studying the property of water inside an ultra-high vacuum chamber that also houses a high
voltage electron gun, a highly sensitive mass spectrometer, and several ion gauges adds more challenges
to the task. In reality, all these expectation or difficulties only make the project more irresistible. In this
chapter, we first introduce the long-time curiosity on water, and then present the modification and
enhancement implemented for this water experiment. Finally we discuss the result and prospect of the
project.
93
6.1 Structure and Dynamics of water
Water is often perceived as ordinary since it is ubiquitous in the world. It is composed by two
common reactive elements, two hydrogen atoms attached to a single oxygen atom. It can act as a solvent,
a solute, a reactant, and a biomolecule that provides structure for proteins, nucleic acids, and cells.
Despite its simplicity in composition and small size, it is the most extraordinary substance as the
existence of life on Earth depends on its special properties that nurture everything we know. Simply put,
life would not exist without the presence of water.
Despite water being the second most common molecule in the Universe, right behind hydrogen,
many of its properties are not well understood. When comparing to the hydrides of neighboring element
near oxygen, the water boiling point is out of the trend. Following the trend from the periodic table, water
should be in a gaseous form at 1atm. In its liquid form, it does not behave like other liquid either. Its
density reaches a maximum at 4 oC in liquid form, which is not typical. Often liquids have higher density
in the solid phase. The compressibility of water is minimized at 46.5C as other liquids usually get more
compressible when heated up. Its viscosity decreases as higher pressure is applied, which is in the
opposite trend of other liquids. Under pressure, the melting point and maximum density point of water
shift to lower pressure, which is again at odds with other liquids. Since Rontgen, 1901 Nobel Laureate,
suggested a mixture of ice dissolved in monometic water in 1891 [Ron 1892], the study of state and phase
transition of water has sparked much interests and debate.
In his “Structure of Liquid Water” paper, Rontgen believed the anomalous properties of water can
be explained if we assume that “liquid water consists of two types of molecules with different structures.
Molecules of the first type, which we would like to call ice molecules since we are going to ascribe to
them some properties of ice, undergo transformation into molecules of the second type when the
temperature is increased. Thus, we consider water at any temperature as a saturated solution of ice
molecules whose concentration is higher when the temperature is lower.” His paper described for the first
94
Figure 6.1.1 Purposed structure of water (a) LDL and (b) HDL [Cha 1999].
time what is known as the two-structure model of water. In the subsequent hundred years to come, his
two-state postulate has evolved into an equilibrium between two types of structures, often called low-
density liquid (LDL) and high-density liquid (HDL). It is believed that these structures LDL and HDL
form hydrogen-bonded network with localized structure and clustering, illustrated as Figure 6.1.1(a) and
(b), respectively. .
Numerous experiments have tried to observe the existence of two-state water. Huang and
colleagues [Hua 2011] used X-ray to study water structure at different temperatures. The intermolecular
pair-correlation function (PCF) g(r), shown in Fig. 6.1.2, shows an increment in intensity at 3.3Å, which
correlated to high-density water clusters with increasing temperature. At the same time, they also
observed a diminishing intensity of the dome at r=4.5Å that corresponds to the O-O distance that does not
occur in the dense ice form with increasing sample temperature. Both of these phenomena points to a
transformation or transition of LDL into HDL, however, the result is not conclusive due to possible
truncation or background subtraction during their data analysis.
In 2003, Wang and his colleagues studied the spectral diffusion in the OH stretching band of
(a) (b)
95
Figure 6.1.2 Optical studies on water (a) comparison of g(r) of liquid water measured at 7, 25, and 66
oC
with X-ray. (b) Raman spectra with 3115 cm-1
pumping, fit using the two Gaussian sub-bands V(red)
and V(blue). (c) Time dependence of red and blue band with 3115 cm-1
pumping at different temperature.
water, the transition, using ultrafast IR-Raman spectroscopy. The Raman spectra, shown in Fig.
6.1.2., exhibits ps dynamics at two peaks, marked as red and blue, associated with O-H bond stretching in
water. However, like many Raman spectroscopy result, the fitting of the spectra and assignment of the
bands can be controversial, and it lacks the direct observation of lattice structure.
With the molecular beam doser that deposits water onto the sample surface in our ultra-high
vacuum chamber[Mur 2009], a low-vibration cryogenic sample holder that goes down to 20K, and
(a)
(b) (c)
96
ultrafast electron crystallography with wavelength-tunable excitation laser, we are poised to study the
structural dynamics when water sublimates at low temperature.
97
6.2 Experiment Setup
The UEC experiment setup for ice/water observation, shown in Fig. 6.2.1, is very similar to that
used for CDW material, described in section 3.3, except for the usage of the molecular beam doser and
the 3000nm laser utilized for hydrogen-bond excitation. The ultrafast pump-probe is driven by a
Ti:Sapphire femtosecond laser system that delivers 2.5mJ/cm2, 50fs, 800nm laser pulses at a 1kHz
repetition rate. The output pulses are split into two paths, pump and probe, by a beam splitter. The laser
pulses along the pump path drive an optical parametric amplifier (OPA) that generates a board range of
selectable optical wavelength, from 285 to 2700 nm. The laser output from this OPA is further combined
to generate the 3000 nm laser that is in tune with the vibration mode of hydrogen bond in water. The
method of generating this mid-infrared is detailed in section 6.3. The laser pulses along the probe path
are frequency-tripled into ultraviolet pulses (266nm, 4.7eV) that drive the fs photoemission from a
Ag photocathode to form the probe electron beam. The photoelectrons are consequently accelerated to
20-40 keV and focused by a short-focal distance magnetic lens into a 5-30 µm narrow probe to interrogate
the nanoscale water layer by the way of electron diffraction [Rua 2007].
The ultrafast electron diffraction technique for the water experiment is identical to that used in
CDW materials, described in section 3.3.
The diffraction pattern from ice/water resembles the powder diffraction type from randomly
oriented water crystals formed on substrate. In the reflective diffraction geometry, shown in Fig. 6.2.2(a),
the electron "bounces" off the ice/water layer on silicon and diffracts to the CCD camera. The main
advantage of the reflective diffraction is the ability to interrogate a larger sample area thanks to the small
incident angle, typically 0.5 to 5o. However, in this geometry, due to the existence of a supporting
substrate, the diffraction cone is cut into half by the shadow edge, equivalently losing half of the
98
Figure 6.2.1 Experiment setup. (a) Experiment setup for ice/water related experiment. Different
diffraction geometry and corresponding water diffraction image obtained on CCD camera in reflection
diffraction setup and (b) transmission diffraction setup.
experimental signal. Additionally, due to this larger footprint of probed area, the arrival time of the pump
laser would be slightly different within the sampling area, which increases the time resolution in the
experiment. On the other hand, in the transmission geometry shown in Fig. 6.2.2(b), the electron
penetrates through the sample and substrate to form the diffraction image on our CCD camera. The time
resolution is minimized because of the small size of the sample area, equivalent to the size of the electron
probe. However, the experimental signal is also reduced because less ice/water crystal is sampled.
The ice/water layer on substrate is delivered via our molecular beam doser built by Dr. Ryan
Murdick [Mur 2009]. The water is injected onto the substrate surface at 90 K in an ultra-high vacuum
(a)
(b) (c)
99
environment, and ice crystals are formed within a few hours after the water dosing. More detail regarding
the ice/water layer formation can be found in section 6.4.
I would like to thank Peter Lee for designing the cryogenic sample holder that made this project
possible. Peter's innovative design on the sample holder enabled us to conduct experiment at T = 14K
while maintaining the pump/probe access to the sample and the 4-axial freedom of sample movement.
100
6.3 Generation of Mid-IR Excitation Laser via Nonlinear Optics
One of the most direct methods to study the dynamics of the water network is to excite the OH
stretching vibrations [Cow 2005] [McG 2006], which are strongly coupled with the Hydrogen bonding
that is associated with the distribution of hydrogen-bonded structures and the intermolecular forces that
dictate the structural dynamics of the liquid [Fra 1972]. In simplest term, the vibration modes of OH
bond in water can be mainly characterized by the symmetric stretch , bending , and asymmetric
stretch modes, illustrated in Fig. 6.3.1(a). The frequency associated with these modes ranges from
3210 to 3755 cm-1
for and , and 1595 to 1670 cm-1
for the mode across a wide range of
temperature, summarized in Table 6.3.1 [For 1968]. However, our OPA can only output laser light with
frequency > 3700 cm-1
, or < 2700 nm in wavelength. Therefore, we have to generate the ~3000 nm mid-
infrared by building additional nonlinear interaction using the available output provided by OPA to excite
OH stretching modes.
Long before the invention of the laser, the nonlinear-optical effects have been observed in, for
example, Pockels and Kerr electro-optic effect [Boy 2003] and light-induced resonant absorption
saturation, described by Vavilov [Val 1950]. However, the optical nonlinearities only broadened its
catalog after the advent of lasers that provided the much needed intensive energy for such a phenomena.
In 1961, Franken et al. [Fra 1961] first observed the nonlinear optical effects, the second harmonic
generation (SHG), in the laser era. During next year, 1962, Terhune et al. first reported the observation of
third harmonic generation. Then in the next four decades, the field of nonlinear optics has experienced an
enormous growth, leading to the observation of new physical phenomena and giving rise to novel
concepts and applications. The nonlinear-optical concept can be found in many excellent textbooks by
[She 1984], [Boy 2003], [Cor 1990], and [Rei 1984].
Nonlinear optical phenomena occurs when the response of a material systems to an applied field
depends in a nonlinear manner on the strength of the optical field. The induced dipole moment per unit
volume, or polarization , of a material depends on the strength of of an applied external optical
101
Figure 6.3.1 OH vibration modes of water. (a) Illustration of three vibration modes in OH bond of water.
(b) Experimental observed frequency for OH vibrations in water [For 1968]. The corresponding
wavelength for some frequency is listed in red.
field. In the case of conventional, or linear, optics, the induced polarization depends linearly on the
electric field strength that can be described by
. .1
where is known as the linear susceptibility and is the permittivity of free space. In nonlinear
optics, the optical response can often be described by a more generalized Eqn. 6.3.1 by expressing the
polarization as a power series in the field strength as
. .2
The and are known as the second- and third-order nonlinear optical susceptibilities, respectively.
When we treat the fields in a vector nature, then becomes a second-rank tensor, becomes a third
(a)
(b)
(2967 nm) (2990 nm) (3003 nm) (3021 nm)
(3058 nm) (3082 nm) (3096 nm) (3115 nm)
102
rank tensor, and so on. Here we have assumed the polarization at time t depends only on the
instantaneous value of the electric field strength, and the medium must be lossless and dispersionless. At
the same time, the and are referred to as the second- and third-
order nonlinear polarization. In general, the second-order nonlinear optical interactions can occur only in
non-centrosymmetric crystals, namely crystals that do not display inversion symmetry. On the other hand,
third order nonlinear optical interactions can occur for centro- and noncentrosymmetric media.
When we represent the electric field in the form of a sum of two monochormatic waves, or
. .
the second-order nonlinear polarization of a noncentrosymmetric material can be written as
. .4
Eqn. (6.3.4) can also be expressed in
. .
We can express the complex amplitudes of the various frequency components of the nonlinear
polarization as
second harmonic generation SHG ,
second harmonic generation SHG
sum frequency generation SFG
difference frequency generation DFG
optical rectification R . .
The process of SFG, which is illustrated in Fig. 6.3.2(a) and (b). The process of SHG is just a
special case of SFG with which is useful to produce radiation in the ultraviolet spectral
region. On the other hand, DFG, illustrated in Fig. 6.3.2(c) and (d), can be used to produce infrared
radiation. By following the energy conservation in the interaction, we can relate the wavelength of each
wave in SFG or DFG using
103
Figure 6.3.2 Different nonlinear process. (a) Geometry of sum-frequency generation. (b) Energy-level
description of SFG. (c) Geometry of difference-frequency generation. (d) Energy-level description of
DFG [Boy 2003].
for SFG or
for DFG . .7
One can readily control energy of the output laser by choosing the appropriate energy level of input
waves. Typically the three waves involved in SFG and DFG interactions are named as pump, signal, and
idler according to their respective wavelength,
. .9
(a) (b)
(c) (d)
104
In Eqn. 6.3.6, there are four nonzero frequency components and all those these four are present in
the nonlinear polarization. However, typically one of these frequency components will be dominate in
the intensity. It is because the nonlinear polarization can be efficiently produced if a certain phase-
matching condition is satisfied, and usually this condition cannot be satisfied for more than one frequency
component. Practically, one can choose the desired frequency component by adjusting the polarization of
each waves by the phase-matching condition,
. .
via orientation of the input waves
By examining the availability of our TOPAS output wavelength, it is the most direct to utilize
1256 nm and 2165 nm lasers from TOPAS to generate 2991 nm, which is chosen to directly excite the
OH vibration modes and of ice at low temperature, as listed in the Fig. 6.3.1, through the DFG
interaction, Eqn. 6.3.7,
1
12
1
21 =
1
2991 . .10
The optics setup to generate the ~3000 nm laser beam for the OH vibration in water is illustrated in Fig.
6.3.3. In Figure 6.3.3, our OPA is driven by a Ti:Sapphire femtosecond laser system with 1.0 mJ/cm2,
~50fs, 800 nm pulses at 1kHz repetition rate. Using this source, OPA can be adjusted to output a 1256
nm signal beam at ~200 µJ/cm2 (shown in green color in Fig. 6.3.3) and 2165 nm idler beam at ~97
µJ/cm2 (shown in red) in order to generate the 3000 nm laser at the nonlinear crystal AgGaS2 (part
number AGS-401H from Altos photonics). We use the 1st delay stage in the 2165 nm laser path to
optimize the temporal overlap of two input lasers. At the same time, a dichroic mirror (DM), which
allows 2165 nm to pass through while reflects 1256nm laser, is placed in the path of both so they can be
directed to the AgGaS2 crystal for DFG interaction. Since all three lasers involved here are not visible,
the optimization of the alignment can be tedious.
A step-by-step procedure is listed below as reference:
105
Figure 6.3.3 Optics path and setup for mid-IR generation. The green line indicates the 1256 nm optical
path. Red line represents the 2165 nm laser path. The blue path is where the 3000 mid-IR travels. The
M1 to M7 mirrors are purchased for the high reflection on 1256 nm and 2165 nm, while M8-M12 are Au
coated exhibiting low loss for the infrared range. The purple arrows indicate the polarization of each
wave.
1. Optimize output power from TOPAS. To optimize TOPAS output, one should minimize the
pulse temporal width of 800nm. This can be roughly achieved by optimizing the 266 nm output
from our tripler.
2. Roughly match the optical path length of signal and idler, so the temporal overlap of both lasers
on the nonlinear crystal is not far off.
3. Place the nonlinear AgGaS2 crystal with 5 deg tilt from vertical [(phase matching angle ~ 44o) -
(cutting angle ~39o)]
4. Make spatial overlap between signal and idler on the AgGaS2 crystal.
106
a. Place a long-pass filter right after DM to minimize those visible lasers below 1000nm
that may interfere the visual inspection of those invisibles.
b. One can visualize the location of the signal, idler, and 3000 lasers on a thermochromic
liquid crystal sheets that would changes color with heated by the incident lasers.
5. With temporal overlap (adjusting 1st delay stage) and spatial overlap (adjusting 2 mirrors right
before DM and DM) both close to optimal, try to locate a 800nm laser between the signal and
idler after the nonlinear crystal. This 800 nm is generated by SFG from the signal and idler since
all components in Eqn. 6.3.6 do occur in the nonlinear process. Since SFG is more efficient than
DFG, this 800 nm is much easier to locate, and can be used as an indicator for optimizing the
temporal and spatial overlap.
6. Once the 800 nm from SFG is close to optimal, one should be able to locate the mid-IR 3000 nm
near the signal spot using a thermochromic liquid crystal sheet.
7. Remove the long-pass filter. Optimize the 3000nm power by adjusting the delay stage, mirrors,
and tile angle of AgGaS2 crystal.
The maximum power of the 3000 nm beam we can achieve is 13 µJ/cm2, that represents a
conversion efficiency of 6.5% ( the power of 3000nm / the power of 1256nm signal ) which is on par
with that obtained by Prof. McGuire (7.0%) who taught us invaluable knowledge when he guided us
through the alignment process at the inception of our mid-IR optical setup. At the same time, we would
like to acknowledge Dr. Kim for setting up this optical path for mid-IR generation and getting us a good
start on future experiment.
Because the OPA output is adjusted to be diverging by the manufacturer for safety reason, the
3000 nm laser beam also exhibit an increment in size. To decrease the energy lost due to this widening,
we place the 1st focusing lens right before the 2nd delay stage to slightly focus the mid-IR so it will not
expand larger than our mirrors and lens downstream. When the 3000 nm pump enters the chamber via
high-transmission viewport, it sustains intensity greater than 4 µJ/cm2.
107
6.4 Ice/water Deposition on Substrate Using Molecular Beam
Doser
In order to preserve the pristine property of the sample, in surface science it is common to grow,
synthesize, or deposit the desired sample in-situ to the substrate in the same location or environment
where the experiment would be conducted. To study ice/water in our UEC setup, depositing the water
directly to the substrate in a UHV chamber is the only viable but very challenging method [Rua 2004],
especially because we cannot use an enclosed cell to hold water sample because we need to preserve the
direct access and exit path for the electron beam to sample. In addition, delivering water without
damaging the 30 kV electron gun, mass spectrometers, and ionization gauges in the same UHV chamber
is not a trivial matter. In 2007, Dr. Murdick, an alumni from our group, installed the molecular beam
doser with fine and quantitative control of delivering molecular gas onto the surface under UHV[Mur
2009].
To determine the proper sample temperature for the experiment, we first perform a few dosing
tests and monitor the water traces reported by our quadrupole mass spectrometer (QMS). By varying the
dosing time, we deliver a variable amount of water onto our sample holder at < 100 K, then we warm up
the sample holder temperature slowly, ~1 K / min, while recording the QMS readings for water, or at the
mass-to-charge = 44. The result, plotted in Fig. 6.4.1, shows the ice/water starting to desorb or sublimate
from the sample holder at ~140K consistently, regardless of the amount of water in the system. The total
amount of water detected by the QMS, total area under the curve in Fig. 6.4.1, is proportional to the
dosing time with a constant dosing rate. With more water dosed onto the sample holder, the shift in the
overall profile in the desorption measurement with respect to the sample holder temperature can be
rationalized by the thicker layer of water that would require higher temperature to desorb completely.
With this universal desorption temperature, 140K, we can calculate the sublimation pressure using the
formula in the literature [Wag 2011],
108
Figure 6.4.1 The water sublimation measured by from QMS as temperature rises with different dosing
time.
with
where and with and ; and are
the values of the normal triple point (Solid-Liquid-Gas). Using 140 K for Eqn. 6.4.1, we calculate
the sublimation pressure torr, which agrees very well to the pressure measured by
ion gauge in our UHV chamber.
The water can be dosed onto many substrates of choice, depending on the desired experiment
geometry, explained in section 6.2. For reflective diffraction geometry, we have successfully deposited
water on pure silicon, silicon oxide, nanocavity on silicon, graphite, and on to a gold nanoparticle
decorated silicon substrate. Visually, the ice/water layer can be observed on a pure silicon substrate,
shown in Fig. 6.4.2 (b), comparing to the pristine silicon chip before dosing, shown in Fig. 6.4.2 (a). For
109
Figure 6.4.2 The pure silicon mounted on sample holder (a) before and (b) after water dosing. (c) Optical
image of thin amorphous silicon membrane (blue area) manufactured on a silicon substrate (grey
background). (d) Thin amorphous silicon membrane sample mounted (circled in red) onto our sample
holder ready for transport into our UHV chamber for transmission diffraction experiments.
the transmission diffraction geometry, we can deposit water on a thin layer (20nm) of amorphous silicon
film that was originally intended for suspending samples for TEM observation, shown in Fig. 6.4.3.
The deposition process can be monitored more precisely by the electron diffraction pattern from
the sample using a glazing angle. For example, when water is deposited on the AuNP decorated silicon
substrate, the diffraction pattern from AuNP will get obscured when nanoparticles are covered by the
dosed water and ice, shown in Fig. 6.4.3 (a), (b), and (c). The same observation can be made during
(a) (b)
(c) (d)
110
Figure 6.4.3 Pictures from water experiment. (a) The diffraction pattern from AuNP decorated silicon
substrate at room temperature. (b) When the amorphous water starts to cover the AuNP and obscure the
AuNP diffraction, water dosing can stop, taken at T = 115 K. (c) A few hours after water dosing is
stopped, the amorphous water self-assemble into crystal form at 115 K. (d) Diffraction pattern from
silicon with nanocavity at room temperature. (e) Scattering from water starts to replace the nanocavity
pattern, taken at T = 78 K. (f) Fully crystallized water completely cover the Si substrate with nanocavity,
taken at T = 127 K. (g) Diffraction pattern of ice yields to that from Si nanocavity when ice starts to
sublimate at T = 157 K. (h) The diffusive diffraction pattern from amorphous silicon membrane at T =
115 K. (i) Diffraction pattern from ice and amorphous silicon membrane. (j) SEM image of nanocavity
on silicon substrate.
(a) (b) (c)
(d) (e) (f) (g)
(h) (i) (j)
111
dosing water onto other substrates in the reflective diffraction geometry, like silicon with nanocavity,
shown in Fig. 6.4.3 (j). The diffraction pattern from the substrate is replaced by the random scattering
from amorphous water layer first, then completely obscured by the diffraction pattern after the amorphous
water self-assembles into crystal ice, illustrated in Fig. 6.4.3(d) to (g). In the case of water crystal or ice
transmission diffraction experiments using an amorphous silicon membrane, the electron beam would
penetrate all the sample in its path, and the diffraction pattern recorded on our CCD camera is the sum of
that from the membrane and ice crystal, illustrated in Fig. 6.4.3 (h) and (i).
112
6.5 Ice/Water Experiment Result
Figure 6.5.1 Reflective diffraction experiment on water. (a) Reflective diffraction geometry with ice
deposited on pristine silicon and typical diffraction pattern from ice layer. (b) Intensity ratio dynamics of
ice (111) + (200) triggered by 3000nm laser, f = 4.5mJ/cm2, at T = 130K.
Because the larger footprint of a probe on the sample can lead to a larger pump-probe spatial
overlap and more diffraction signals from the wider sampling area, we start conducting the experiment
using 3000 nm excitation laser on ice in reflection geometry, depicted in Fig. 6.5.1(a). With 4.5 mW
power delivered on the ice surface and an expected 300 µm width in size, the mid-IR laser applies fluence
~ 4.9 mJ/cm2 on the ice layer at T = 130 K. As presented in Fig. 6.5.1(b), the change of intensity at the
ice (111) + (200) ring, or the first intense ring shown in the diffraction pattern in Fig. 6.5.1(a), shows a
fast decay and recovery that yields the sign of lattice fluctuation. The whole dynamics of decay and
recovery took less than 15 ps to complete and exhibit a maximum of ~ 4% change in the integrated
intensity of that ice (111) + (200) ring. However, due to the low power of the mid-IR laser and the
smaller excited/probed area ratio inherent in the reflective experiment geometry, we could not generate
higher change in order to examine this dynamics in detail. The main advantage of the reflective
diffraction geometry is being able to cover a large sample area using a glazing incident angle for electron
beam. Although the large footprint, which can be as greater than 1.7 mm long with a 30µm electron
beam and 1o incident angle, provides stronger diffraction intensity by sampling larger area, it would
(a) (b)
113
Figure 6.5.2 Transmission diffraction experiment on water. (a) Geometry of transmission diffraction
experiment. (b) Diffraction profile obtained before (red curve) and 2 ps after (blue curve) the excitation
laser hits the ice sample. The +2ps profile has been scaled to compare with that before mid-IR lands on
sample.
almost necessarily require a larger pump laser to excite the longer sampled area.
With enough pump laser power, we can expand the size of the excitation laser on the sample
surface so most of the sampled area is excited in order to obtain a high signal of reaction from material.
With finite laser power, we can choose to excite a smaller area with higher fluence or a broader area with
weaker fluence. Either scenario, however, would still generate less-than-desired signal when working
with a less powerful excitation laser, for example our mid-IR, 3000nm laser.
With the transmission diffraction geometry, depicted in Fig. 6.5.2(a), we expect the probed area
can be fully covered by our 300µm mid-IR pump since the sampled area is the same size as the probe, ~
30µm in diameter. With the electron beam penetrating through the ice layer and the amorphous silicon
membrane, the diffraction pattern presents a 3/4 circular powder diffraction rings on our CCD camera,
shown in Fig. 6.5.2(a). Since we have the diffraction pattern of the amorphous silicon membrane itself,
shown in Fig. 6.4.3 (h), we can obtain the diffraction intensity solely from the ice layer by subtracting the
contribution generated from the silicon membrane. Fig. 6.5.2(b) displays the radially integrated
diffraction intensity from the ice layer showing the profile of the diffraction pattern before the excitation
(a) (b)
114
laser illuminates on the sample (red curve) and the change in intensity observed at +2 ps after the mid-IR
hits (blue curve). For comparison, we multiply the change in diffraction rings 33 times to show the
observed change at +2 ps is indeed that from ice layer. The results translates to a ~1% drop in ice
diffraction intensity after our 3000 nm laser illuminates the surface. However, the experiment time
cannot be sustained long enough for us to study this dynamics in detail due to the excess vibration in our
sample cooling mechanism. The sample used in our experiment is mounted at the very end of > 5' long
cryogenic column, and the minute vibration at the motor that cycles helium gas into the cooling column is
amplified at the sample end. A rough measurement yields a > 40µm vibration at the sample surface,
which is sufficient to displace the sample out of the electron probe or change the fluence on the surface
dramatically by moving the sample away from the peak of pump profile.
From the optical constants of water reported in literature [Hal 1973], which states the extinction
coefficient of water with 3000 nm laser is 0.272. The absorption coefficient can be calculated via
11388 cm-1
, and this value leads to a ~5% absorption if we consider a 50 nm thick ice layer.
Then the expected temperature change of a 50 nm thick ice layer, specific heat 2.03 J/goC, when
illuminated by a fluence ~ 5mJ/cm2, 300 µm wide, 3000 nm laser is less than 0.1 K. Without having a
higher power of 3000 nm laser, we can try to study a thinner ice layer, which may lead to lower
diffraction intensity, while at the same time conduct the experiment at a temperature closer to the
sublimation point, ~140 K. By combining 1) the high brightness electron beam already realized by the
UEM project in our group, which can provide sufficient diffraction intensity from a thinner ice sample, 2)
the base temperature closer to sublimation point, and 3) the low-vibration cryogenic system, which is
already implemented in the 1T-TaS2 experiment described in chapter 5, we should then be able to
elucidate on the age-long questions concerning the two-structure water in the near future.
115
CHAPTER 7
Surface-Plasmonic-Resonance Enhanced Interfacial
Charge Transfer
Interfacial charge transfer has been hard to monitor because of the fast time scale of carrier
transfer, the meso- or nanoscale dimension, and the difficulty creating a reliable metal contract for
electrical measurement. In this chapter, we present our photovoltammetry technique that allows us to
quantitatively measure the charge redistribution, the direction of carrier flow, and the sequence of events
at a heterogeneous interface that contains three elements: gold nanoparticle, silicon, and an ice/water layer.
116
7.1. Introduction
To understand the fundamental processes in the new type of solar cells and photocatalysis that
incorporate nanomaterials [Gra 2003] [Har 1997] and molecularly engineered interfaces [Ash 2002], it is
important to be able to characterize the photoinduced charge dynamics in the nanostructures and
interfaces. These photo-driven devices utilize the interface-induced carrier separation to minimize the
recombination of the photogenerated electron/hole pairs and improve the sensitization by the visible light
spectrum through controlling the size, dopant, and surface plasmonic effect [Shi 2000] [Mil 2004] [Luq
2007] [Les 2007] [Kon 2008] [Hua 1997] [Cal 2004] [Bac 1998] [Aro 2001]. At the nanomaterial
interface, the migration of carriers from the sensitized interface region to the metal contact is driven not
only by the local electrochemical potential difference, but also by the decay rate of such photoactivated
carriers in the transport process. As the device dimension approaches several nm scale [Ada 2003] [Avi
1974] [Avo 2007] [Bez 1997], shorter than the mean free path of electron, ballistic transport becomes the
dominant channel, the carrier trapping and recombination at the interface becomes the central issue to
investigate [Mar 1985] [Che 1993] [Dat 1995]. These processes are difficult to characterize directly due
to the fast time scale, minute dimension, and problems associated with forming reliable contact for
electric measurement. While several ultrafast optical techniques have been applied to investigate the
electron dynamics at the interfaces [And 2005] [Mil 1995] [Kub 2005] [Pen 2005] [Tan 2012], they are
usually not well tuned to measure the photo-conductivity at the interface. Using the sensitivity of the
diffracted electron beam to the local electric field, or ultrafast diffractive photovoltammetry technique
[Mur 2008] [Rua 2009] [Cha 2011], we can observe the charge redistribution processes at nanomaterial
interfaces induced by photoexcitation without contact at ultrafast time scale.
With our photovoltammetry, we investigate three prominent charge transport process, depicted in
Fig. 7.1.1: (1) Dielectric realignment: the alteration of alignment of dipolar elements, in dielectrics creates
displacement filed without carrier current in the materials. (2) Carrier diffusions: the photocarriers
117
Figure 7.1.1. Charge redistribution at interface after photoexcitation. (a) dielectric realignment. (b) carrier
diffusion. (c) interfacial charge transfer.
generated in the photoexcited region diffuse to the unexcited region and induce internal photocurrent. (3)
Interfacial charge transfer: The photoexcitation alters the balance of chemical potential at the material
interface, resulting the change transfer to counteract the change in free energy. The decay of these
photovoltages may involve drift, dipolar relaxation, carrier recombination, diffusion, and radioactive
decays.
(a) (b) (c)
118
7.2. Ultrafast Diffractive Photovoltammetry Methodology and
Experiment Setup
The experiment setup for the ultrafast photovoltammetry is the same as the ultrafast electron
crystallography with reflective diffraction setup (see section 6.2.). The only difference is the method of
data analysis. At the core of the photovoltammetry measurement, the link between photocurrent and the
responding transient surface voltage is established via field integration. To evaluate , we
consider a slab geometry, Fig. 7.2.1., that provides a basic framework for describing the transient-field-
induced refraction of the diffracted beams. In the simplest concept, our photovoltammetry measures the
photoinduced surface field that is required to "refract" or "bend" the diffracted electrons. In Fig. 7.2.1,
the top trajectory is the electron scattering from the crystal planes without the presence of a surface field.
The electron beam with initial energy e , incident at , is Bragg scattered at , exiting the surface at .
When a surface potential , created by the charge redistribution that induced from photoexcitation, is
presented in the electron path, the incident electron beam would be refracted deeper into the crystal at .
The Bragg diffracted beam would get affected the same way and the electron beam would ultimately exit
the crystal at with a net shift relative to on the CCD. The induced angular shift in the
diffraction pattern can be calculated by
7.2.1
where
7.2.2
7.2.
119
Figure 7.2.1 The slab model for transient surface voltage.
It is important to note the difference between the refraction-induced shift and the structurally relevant
shift. The shift in the reflection peak position, following Bragg's law, should increase linearly with the
scattering order in the reciprocal space. In contrast, the refraction-induced shift would show a
nonreciprocal relationship with respect to the exiting angle More detailed derivation and discussion
on ultrafast diffractive photovoltammetry can be found in our publication [Cha 2013].
The experimental setup for measuring surface voltages of nanoparticles and interfaces is similar
to those described in section 6.2, but replacing the pure silicon with a nanoparticle decorated Si surface.
As described in section 6.4., we deliver a layer of water-ice on the nanoparticles by vapor dosing at 90K
using the doser. The steady growth of ice is monitored by the glazing incident electron beam until the
signal of the gold diffraction is replaced by an ice pattern. This gives the rough estimate of the thickness
of water-ice layer to be around 50nm, or roughly the same as the diameter of AuNP particles.
120
7.3 Charge Transfer between Nanoparticles and Substrate
Enhanced by Surface Plasmon Resonance Excitation with the
Coverage of Water-Ice
The application of a water-ice layer that completely covers the nanoparticles-decorated interface
can alter the incident photon resonance structure with the evanescent SPR field strongly coupled to the
dipole moments of the surrounding water molecules. The modified resonance structure will impact the
SPR-induced charge carrier dynamics, and it has great impact in searching the optimal geometry to
enhance the performance of composite photocatalysis that incorporates semiconductor and plasmonic-
metal nanostructures. Recent studies found strong positive correlation between SPE and reaction rate,
leading to a hypothesis that the metallic SPR enhances rates of photocatalytic reaction at nearby
semiconductor surface through carrier redistribution at the interface [Lin 2011]. With a sample of the Au
nanoparticle on silicon substrate covered with dosed ice/water, we examine various channels that
energetic charge carriers travel at metal/semiconductor/water-ice interface. We can then understand SPR
enhancement effects. We apply a scan of the pump laser wavelength from 800nm to 400nm using our
optic parametric amplifier. Over a time span up to 1000ps, we deduce the surface voltage of the ice layer
from the refraction shift of ice diffraction pattern, as described in section 7.2 and [Cha 2013]. The result
of time vs. wavelength photovoltage response map is constructed as shown in Fig. 7.3.1.
From the time-slices across the map at representative = 400, 470, 525, and 585nm, the spectral
evolution can be seen as encompassing two temporally separated process: one that commences at 0 ps
and decays greatly within 100ps, and the second one that rises as the first one decays without relaxation at
all within the observed time scale 1000ps. Slicing the response map at 30ps and 100ps, shown in Fig.
7.3.1(b), we see the photovoltage spectrum evolves from initially a singular peak at 525nm to 585nm at
~30ps, which mainly describes the fast process in dynamics across the spectrum. On other hand, at
121
Figure 7.3.1 Charge redistribution spectrum. (a) Surface photovoltage response map constructed using
the diffractive voltammetry conducted on the water-ice surface covering gold nanoparticles/SAM/silicon
interface at excitation wavelength from 400 to 800nm. Four selected surface photovoltage shown in
white curves, at = 400, 470, 525, and 585nm, demonstrate a composition of two dynamics with
different timescales. (b) comparisons between the surface voltage response spectra obtained from the
interface without the coverage of water-ice (black line), ones with water-ice layer showing a red shift of
the resonance peak (green line) at 30ps, and the bifurcation of peaks (blue line) at 100ps.
~100ps, the dual peak structure with an additional peak at 470nm presents the second process of the
dynamics with different excitation wavelength. The shift of the dipole resonance peak from 525nm to
585nm can be understood by finite difference time domain (FDTD) simulation and contributed to a strong
coupling between the SPR of the nanoparticles and the surrounding water dielectrics. However, the
presence of high-energy response at ~470nm appeared at 100ps cannot be produced from the optical
domain calculation alone. Such short-wavelength mode is typically of high-order and is not optically
active at particle size less than 50nm.
Figure 7.3.2 shows the result of the controlled experiment in which the photovoltage at the ice
surface is measured without the presence of Au nanoparticles, in order to disentangle the two different
dynamics observed in Figure 7.3.1(a). Without the Au nanoparticles on silicon substrate, we observe a
(a) (b)
122
slow dynamics that is very similar to the second dynamics component with the presence of nanoparticles,
but without the fast dynamics. This result reveals the slower process, red curves in Fig. 7.3.2, is in fact
the charge carrier dynamics launched purely from the silicon substrate. Since the dielectric property of
ice is unlikely influenced directly by visible light excitation, the apparent delay in the voltage rise on ice
surface from the controlled experiments is indicative of a long-range charge carrier injection from Si into
the ice surface. At the same time, the shortening of such an injection time as the photon energy increases,
from 800nm to 400nm, is particularly interesting. The dependence of this delay on photon energy and the
high charge drift velocity, ~1nm/ps, also support that the origin of energetic carrier injection is indeed
from Si. When reaching the ice surface, the carriers dissipation takes a significantly a longer time (>ns).
Near time zero, we also observe a small and nearly instantaneous downward refraction shift in every
nanoparticles-free free experiment. We attribute this phenomenon to the shift in the chemicall potential at
the ice/silicon interface due to photoexcitation, resulting in a swift change of the dielectric alignment of
the ice layer.
While the slow component in the surface voltage dynamics can be fully attributed to long-range
charging from the substrate, the fast dynamics, plotted in blue circles in Fig. 7.3.2(b), which is completely
absent in the nanopartilce-free controlled experiment, must be mediated by the nanoparticles directly.
The surface field induced by charged Au nanoparticles can be measured on ice surface through dielectric
realignment of the water molecules surrounding the nanoparticles. We can extract this fast charging
dynamics by fully deducting the slow process in the controlled experiment from the overall dynamics,
shown in Fig. 7.3.2(b). Since this fast dynamics reaches maximum before 50ps, the spectrum
representing this long-range-charging by the spectrum-slice shown in green curve in Fig. 7.3.1(b) at 30ps.
The red-shifting, from 525 to 585 nm, of this spectrum at 30ps indicates the charge transfer between the
nanoparticles and the Si substrate is most efficiently driven by the localized dipole resonance fields at the
interface between the two. Furthermore, since this peak at 585nm is present at the 100ps time scale,
shown in blue curve in Fig. 7.3.1(b), this dipole resonance is also responsible for the elevation in the
transfer of energetic electron to the ice surface. This is not surprising since the generation of energetic
123
Figure 7.3.2 Dynamics of induced charge. (a) The controlled experiment with the presence of AuNP for
Ice/AuNP/SAM/Si photovoltage measurement. The rise of the surface voltage is delayed by the timescale
of the charge carriers migrating to the ice surface after being generated from the Si substrate. (b)
Equivalent results obtained the surface with AuNP decoration. By comparing to (a), we can deduce the
fast components (blue circles) unique to the nanoparticles-decorated surface.
carriers at Si surface can also be enhanced by the evanescent waves of SPR in the region. Lastly, it is also
important to notice the appearance of the peak at 470nm in elevating the charge level at the ice surface
indicates that the optically, spatially non-homogeneous higher moment SPR might be activated at the
nanostructural interface [Mah 2012] [Sche 2012] [Che 2011]. Such a high-energy mode excitation, which
is much weaker than the dipole resonance, can play a significant role in the surface charging response
spectrum because the high-energy barrier required for the carrier injection into the ice conduction band
(3.2eV above the Si conduction band edge) significantly suppresses the dominance of the dipole
excitation over such a channel.
The ultrafast photovoltammetry described here can provide direct characterization of charge
transfer at device interface and nanoscale material. Without the interference of the metal contact that is
required for electric measurement, the field-sensitive electron probe provides a clean observation of the
(a) (b)
124
carrier dynamics at femto second time scale. The application of this diffractive voltammetry includes
site-selected studies on nanostructured, SPR enhanced, or heterogeneous interfaces that is crucial in
understanding the delicate play in carrier redistribution.
125
CHAPTER 8
Summary
In the CeTe3 experiment, we have separated the dynamics of two order parameters from ultrafast
structural response to intense optical excitation. From the well separated time scales shown in the
structural suppression, we have concluded the periodically modulated ionic potential well has been
preserved mostly intact during the sub-ps charge melting, hence it can facilitate the rapid recovery of the
electronic order as proposed by others. We believe the well-separated order parameters are due to the
significantly different effective inertia in these two subsystems, and the fact that charge ordering is
directly coupled to the valance electrons that was directly elevated by our femtosecond laser pulses. The
coupling between charges and ions can be reestablished once the hot electron temperature is cooled down
so a stable CDW condensate can recover. We also conclude the fast channel has little to do with the
specific CDW mechanism, which is universally observed by other reports with sub-ps recovery of charge
ordering. Therefore, it is the slower ps structural response following the excitation at electronic part of
CDW provides the distinctions that characterize the CDW family with the stretch of coupling between
electrons and ions. In the case of CeTe3 that demonstrates a fluctuation-dominated phase transition
represents the inherently Peierls-distorted electron-phonon system in CDW.
With 1T-TaS2, a material exhibiting a Mott-Hubbard gap and a nesting-driven CDW gap, we
have presented a new avenue to explore the energy landscape that was not accessible via conventional
methods. With ultrafast photo-doping and carefully chosen excitation energy, we not only drive the 1T-
TaS2 to states previously discovered through chemical doping or high pressure treatments, but also push
the material to other hidden states by traveling a different route on the energy topography. By reaching
126
these meta-table states at sub-ps time scale, we open up the possibility of application with high-speed
low-energy consumption photonic and electronic devices.
With the photovoltammetry technique that can measure charge redistribution and diffusion at
interface quantitatively, we have explored the charge transfer at heterogeneous interface enhanced by
surface plasmon resonance and coverage of ice. We have demonstrated that the technique can observe
the minute charge transfer between three different materials in our sample: gold nanoparticle, silicon, and
ice/water layer. With a flexible experiment setup, we were able to monitor charge redistribution with any
combination of these three materials or as a whole, hence to pinpoint the source and flow of each charge
distribution. At the same time, utilizing our tunable excitation laser and SPR phenomena of nanoparticles,
we sequenced the charge transfer events that was not possible with other technique that requires metal
contact for carrier measurement.
With the capability to study water at its phase boundary, we have explored the possibility of
observing the structural dynamics. We have observed a minute change in the ice structure but could not
study the phenomena in detail due to limitation of laser power and excess vibration issue. However, we
did learned valuable experience along the journey. With the low vibration sample holder already
implemented and proven reliable when utilized in the 1T-TaS2 experiment and the high-brightness of
ultrafast electron microscopy electron source realized by another project in our group, we can expect the
exploration of water unique properties to continue and prosper.
The next experiment following the result of CeTe3 is another anisotropic CDW material: ErTe3.
Belonging to the same Rare Earth tritellurite family, ErTe3 presents two seemingly independent CDW
formation each with its critical temperatures. With ErTe3, we are posed to examine the role of symmetry
breaking, electron-lattice coupling, even CDW-CDW interference with this new material. Regarding the
phase transformation of CDW material, or 1T-TaS2 in particular, we plan to add another dimension to the
phase diagram by studying the doped 1T-TaS2 which has shown a superconducting phase emerging. With
the intimate relationship between CDW and superconducting, one may be able to unveil the cooperation
or the competition between two orders with have-it-all 1T-TaS2.
127
APPENDICES
128
Appendix A Electron Counting and Statistical Uncertainties
Figure A1 Analysis on electron count. (a) The discrete single-electron events recorded on a CCD camera.
(b) The number of occurrences of single-electron events as a function of digital counts recorded for these
events. A mean value of 989 is determined as the analogue-to-digit unit, used to convert the CCD signals
into the electron counts.
To evaluate the statistical uncertainty of the experiment, electron counting is conducted. The
single-electron counting events are established with attenuated electron beam, which are recorded on the
CCD detector, as shown in Fig. A1(a). A total of 1005 such events are counted, and the occurrence of
single-electron events as a function of their digital counts recorded on the CCD is depicted in Fig. A1(b).
The distribution has an average value of 989 digital counts per electron, which we assign as the analogue-
to-digit unit (ADU), used to convert the CCD intensity to electron counts. The number of the electrons
associated with diffraction intensities at thus can be calculated using ,
from which an uncertainty is determined for based on the Poisson counting
statistics. is derived by integrating the digital CCD intensity around the respective diffraction peak,
with the background (thermal noise, incoherent scattering) subtracted by a 2nd
order polynomial fit.
Fig.A2(a) shows the distribution of data at each time stance for the CeTe3 experiment, discussed
in section 4.2, with data acquisition time ranging from 103-10
4 sec. Long integration time is used on 0-2
(a) (b)
129
Figure A2 Statistic on electron counts. (a) The data integration time used for each time stance under
laser fluences F=2.43, 4.67, 7.30 mJ/cm2. (b) The absolute integrated intensity evolution of
CDW superlattice peak in unit of electron counts. (c) The absolute integrated intensity evolution
of main lattice peaks at (0,4) extracted from the same diffraction images as (b).
ps data points to provide sufficient signal-to-noise ratio to investigate the short-time responses. In order
to differentiate the fluctuation effects that have a strong anisotropy, all the reported are extracted
from isolated peaks without averaging equivalent peaks that has the same symmetry at the ground state.
Fig. A2(b) and (c) show and obtained under three different fluences in unit
of electron counts. is extracted from the superlattice peaks at , and
is from lattice Bragg peaks at (0,4). The typical is ~103 e-, while for main Bragg peak ~105 e-.
We note that at F=7.30 mJ/cm2, drops to as low as a few hundred e- counts at ~ 5 ps, resulting
in a relatively large statistical uncertainty.
(a) (b) (c)
130
Appendix B Two Component Fitting and Statistical Analysis
Figure B1 The zoomed in plot of satellite intensity of CeTe3 at early times showing two-step suppression.
The data from F=2.43 mJ/cm2 are multiplied by 3 to compare with data from F=7.30 mJ/cm
2. The error
bars are calculated based on the counting statistics described in Appendix A.
Fig. 4.1.3(a) and Fig. B1 shows the suppression of satellite intensity of CeTe3, expressed in terms
of normalized intensity , where is obtained by averaging the negative time
data (t=-5ps to -1 ps). In Fig. B1 the from F=2.43 mJ/cm2 experiment is scaled up by a
factor of 3 to compare with from F=7.30 mJ/cm2. The inhomogeneity in the decay of
signals is evident from the nonscalability between the two fluences. Both datasets contain a
component with a sub-ps decay and a slower ps component is clearly visible, especially in F=7.30 mJ/cm2
dataset. To describe the different timescales in the suppression of , we fit with a
model consisting of two independent exponential decays and recoveries:
22
22
22
11
11
11
/exp/exp
/exp/exp
1
doro
dr
r
doro
dr
r
ttttA
ttttA
tf
, (B1)
131
where A1 and A2 represent the amplitude of the two-components, represent the respective
decay and recovery times of the two components, and t0 is the onset time. f(t) is coarse-grained by
numerical convolution with a pump-probe cross-correlation function fcc(t), which is modeled as a
Gaussian 22 2/
2
1CCt
CC
CC ef
, where =170 fs is the half-width of electron pulse, estimated
based on the FWHM electron pulse-width: 390±110 fs (Fig. S2). t0, as determined from the fitting, can
shift as much as 200 fs relative to the ZOT established from graphite and between different CeTe3
datasets, which is attributed to the fluctuation of the sample stage m ps during the time-
consuming experiment. The best two component fit on the F=7.30 mJ/cm2 dataset, as depicted in
Fig.B2(a), yields un-coarse-grained = 350±150 fs, = 570±200 fs, = 3.8±1 ps, and a ratio
A1/A2=0.28. Clearly, and are largely resolution-limited, however, the large disparity of the
timescales associated with the two components permits a generally robust determination of the relative
contribution A1/A2. increases at lower fluencies. The validity of two component model is checked
by adjusting A1 from 0 to beyond the best fitted value to assess the difference in . In this exercise, A1
is fixed while other parameters are determined (except , tr1, t0) by fitting. Since at A1=0, Eqn. B1
reduces to a single component model, which has a significantly larger than that of the best fit at
=0.28±0.07, as shown in Fig, B2(b). The optimized has a value of 16.5 (with 15 data points from
t=-2 to 20 ps), which yields a reduced , defined as /(number of data points), nearly 1, indicating that
two component model is statistically sound. The standard deviation = 0.07 associated with A1/A2 is
calculated based on [Bev 1992]:
2
222 2
a (B2)
132
Figure B2 Two component fit. (a) The results of two component fit of experimental S1(t)/ S1(t<0)
data at F=7.30 mJ/cm2 (blue: total, red: first component, black: second component). (b) The value
as a function of =A1/A2 based on fitting S1(t)/ S1(t<0).
In contrast, 2
determined at the single-component limit is more than 3 away, representing a less
qualified model.
We find that datasets from different fluencies can be fitted with nearly the same and
values, but different (ranges from 2.5 ps at F=2.43mJ/cm2 to 3.8 ps at F=2.43mJ/cm
2). Overall,
our results from CeTe3 experiment support the existence of a sub-ps component in the depression and
recovery of PLD, which is directly responsive to the corresponding sub-ps suppression and recovery of
electronic counterpart (CO), widely observed in CDW systems using ultrafast optical and angle-resolved
photoemission spectroscopy techniques.
-1 0 1 2 3 4 5 6 7 8
0.2
0.4
0.6
0.8
1.0
S
1(t
)/S
1(t
<0)
Time (ps)
F=7.30 mJ/cm2
A1+A
2
A1
A2
0.0 0.1 0.2 0.3 0.4 0.5 0.6
15
20
25
30
35
40
45
min=0.28 ± 0.07
Best two component fit
Best single component fit
2
a=A
1/A
2
F=7.30mJ/cm2
S1/S
1 data fit
(a) (b)
133
Appendix C Carbon Nanotube Sample Preparation
A suspended carbon nanotube sample on TEM grid has been implemented and the procedure of
obtaining such a sample is outlined below. A few optical and electronic images are also presented in
Figure C1
1. The multi-wall carbon nanotube (MWCNT) is purchased from Nanolab, Inc, with specification of
15±5 nm in diameter, 5-20 µm in length, and -COOH group functionlization (part number
PD15L5-20-COOH, $130/g).
2. The as-purchased MWCNT material is first suspended in orthodichlorobenzene (ODCB) in a
concentration of 1.5mg per 5g of ODCB. Then the solution is sonicated for 1 hour.
3. Then the sonicated solution is further diluted with concentration of 5 drops per 9 g of ODCB.
4. Sonicate the diluted solution for another 30 minutes until the MWCNT solution contains no
visible solute.
5. The MWCNT can be transferred to a TEM by delivering a few drops of the solution after step 4
onto a TEM grid that is positioned on a filter paper, which helps to guide the solution through the
TEM grid.
6. The density of MWCNT on the TEM grid can be controlled by adjusting the number of drops
applied to the grid.
134
Figure C1 Images of MWCNT. (a) Suspended MWCNT on copper TEM grid. (b) TEM image of a
suspended MWCNT on TEM grid. (c) SEM image of a MWCNT deposited on holey carbon TEM grid. (d)
SEM image of a MWCNT deposited on holey carbon TEM grid. (e) Diffraction pattern from a MWCNT.
(f) Individually separated MWCNT on thin Si membrane.
(a) (b)
(c) (d)
(e) (f)
135
Appendix D Tsunami Alignment
Figure D1 Tsunami fs configuration
The procedure described here should be treated as a supplement to the information in the manual
provided by Spectra Physics. One should read the manual first then use the information provided here as
an aid.
1. Supplement to Front-End Alignment, page 6-2 in the manual.
a. As described in the manual, DO NOT adjust the focus of M3 and M4.
b. Pump beam from Millennium Pro should be positioned at the center of P1.
c. Direct pump beam using P1 and P2 so the pump is centered on the side of M3 and M4
that is CLOSER to the Ti: sapphire rod. This step is crucial to ensure the ease of further
alignment. The pump beam does not need to be located at the center of P2. It is been
observed that the pump beam is usually above the center of P2.
d. Be careful not to put anything in the path of beam near Ti: sapphire rod since it is highly
focused there.
136
Figure D2 Two IR images on M4.
e. Use M2 to center the pump beam on M1.
f. There should be two IR images on M4. Unlike described in the manual on page 6-7, the
image from M3 is a rectangular shape while the one from M1 is a horizontal-orientated
rectangle. (See Fig. D2)
g. One can move the M1 image with M1 and both images with M3.
h. Once these two IR images are positioned on M4, one can remove M4 and view these two
IR images better on wall of the output bezel on figure 4-3 in manual.
i. The proper location of these two IR images has been marked on the output bezel with
marker as a guide.
j. Place M4 back once step h is completed and proceed to Cavity Alignment for a FS
System on page 6-7 in manual.
2. Supplement to Cavity Alignment for a FS System, page 6-7 in the manual
a. Center two IR images on M5 using M4. This step is critical to provide enough travel of
M5 to start lasing.
b. Using M5, guide IRs through Pr1 to Pr4, to AOM, then finally M10. The IRs should go
though Pr1 and Pr4 at the same distance from the edge of each prism.
From M3
From M1
137
c. If needed, one can remove the beam splitter at the outside of output of Tsunami and
observe two IRs at ” away from Tsunami output. Adjust M to center IR spot to the IR
square background.
d. Adjust M10 to start lasing. The output power of Tsunami should increase significantly
once lasing starts.
e. Adjust M1 and M10 to optimize output power.
f. Follow manual to optimize photodiode location and mode-lock.
138
Appendix E Optimization at Spitfire for Optimal Output of Mid-
IR Laser
1) Be sure the pulse train on oscilloscope looks sharp with minimal side peaks on the side of
main pulses. If not, pulse train can be optimized by
a) With Ch1 on and Ch2 off, adjust delay zero in timing menu (service-level control
required) so the pulse train is as far left as possible on scope.
b) Adjust Ch1 so the small peaks between main pulses are minimized.
2) Adjust Ch1 and Ch2 so the build-up time of pulse train is ~62ns. (Measured from the first
peak to the highest one). The shorter build-up time may not provide the highest output from
Spitfire, but it will generate higher TOPAS and 3000nm output down the line.
3) Optimize 266nm output from Tripler with motorspeed.
4) Optimize output from TOPAS with motorspeed, which may be slightly different from that
from step 3)
5) Optimize output from TOPAS with the mirror before TOPAS entrance.
6) Optimize output from TOPAS with time-plate on the side of TOPAS.
7) Optimize 3000nm power by adjusting signal-idler overlap on crystal and delay stage of idler.
139
Appendix F Gold Nano-Particle Deposition on ITO
1) Clean several large glass beakers with Alconox and rinse well with distilled water (DIW) generated
by physics department .
2) Sonicate the needed glasses and Teflon wares in these large glass beakers for 2 minutes and remove
these wares with new gloves onto new kimwipes.
3) Rinse large glass beakers with some Acetone, then sonicate all wares in Acetone for 2 minutes and
remove them with new gloves onto new kimwipes.
4) Sonicate ITO substrate in Acetone, Alconox in DIW, and DIW for 15mins each. Blow-dry with N2
afterwards.
5) Prepare a saturated Sodium Hydroxide (NaOH) by slowly dissolving NaOH pellets in DIW. Immerse
ITO substrates in NaOH solution for 20 minutes.
6) Take out substrates with Teflon tweeters and rinse with DIW with ~3L of DIW.
7) Prepare linker solution. Start with 480ml of DIW, and then add 1ml of Acetic Acid and 5ml of
APTMS while stirring. Immerse ITO chips in this linker solution for 1hr.
8) Take out ITO chips with Teflon tweeters, rinse with DIW with ~3L of DIW, and blow-dry with N2.
9) Prepare Au NP solution. Start with 2ml of DIW, and then add 4 ml of ethanol and 2ml of NP solution.
Immerse chips in Au NP solution for 1 hr.
10) Blow-dry chips with N2.
140
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