non-linear angle-resolved photoemission of graphite: surface and bulk states
DESCRIPTION
Non-linear angle-resolved photoemission of graphite: surface and bulk states. Matteo Montagnese [email protected] , http://www.dmf.unicatt.it/elphos. Università Cattolica del Sacro Cuore Dipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy. Outline. THESIS OUTLINE. - PowerPoint PPT PresentationTRANSCRIPT
Ph.D Thesis defense Brescia, 11 January 2010
Non-linear angle-resolved photoemission of graphite: surface and bulk states
Università Cattolica del Sacro CuoreDipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy.
Matteo [email protected],
http://www.dmf.unicatt.it/elphos
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Introduction
NON-PERTURBATIVE DYNAMICS in SOLIDSGround State and small excitations structure is well understood in many materials
MANY BODY THEORY + QUASIPARTICLE (QP)GS SPECTROSCOPIES + ARPES
WHAT ABOUT EXCITATIONS FAR FROM EQUILIBRIUM?
PULSED LASER APPARATUS – NONLINEAR OPTICAL TECHNIQUES
RESIDUAL INTERACTION BETWEEN QP – BAND RENORMALIZATION – DYNAMICAL EFFECTS
Huang, PRL 80, 197 (1998)
Chemla, Nature 411, 549 2001
STRIVING TO REACH AN UNDERSTANDING & PRECISIONFOR THE EXCITED STATES COMPARABLE
TO GROUND STATE STRUCTURE
EFFICIENT, NON PERTURBING PROBE NEEDED
);(
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Image Potential States
IMAGE POTENTIAL STATES (IPS)
Bound surface states of image potential in samples with a bandgap at
•Pseudo-Rydberg Series in z-direction
•Free-electron parallel to surface: k|| - m =me effective mass (2DFEG)
Adapted from Garcia, PRL 23, 591(1985)
EMPTY STATES – LIFETIME DETERMINED BY THE UNDERLYING BULK( ~ 10-100 fs) BEST STUDIED WITH NL-PE TECHNIQUES
Echenique & Pendry, J. Phys. C 11, 2065 (1978)
Ǻ
C= round trip phase change of the wavefunction
Ph.D Thesis defense Brescia, 11 January 2010
IPS localise in presence of a periodic dipole lattice induced on surface, e.g: C60 on Cu(111) Dutton, JPC 118, 4337 (2003)
Miller, Science 297, 1163 (2002)
Also, IPS dispersion flattens (up to the dispersionless limit) because of transient reorientation of polar adsorbates thanks to the same hot IPS electrons: τLOC≈0.6 – 1 ps
IPS MODIFICATIONS
DISPERSION FLATTENING (m>me)LINEWIDTH BROADENING(EVENTUAL) RIGID SHIFT
')'(' kkk gdkPURE MIXED
Image Potential States
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Graphite
BULK STRUCTURE of GRAPHITE
Optically active in the 3-4 eV region, due to the π bands
van Hove singularity in the J-DOS due to the π bands Saddle point @ M point = HIGH ABSORPTION
Anisotropic: Surface excitations diffuse poorly in the bulk
Lehmann, PRB 60, 17037 (1999)
IPS SENSIBLE TO BULK EXCITATIONS
Electrons
Holes
4.0
-4.0
0.0
π
π*
IPS
Ener
gy (e
V)
SADDLE POINTS
IPS band not fully studied with NL-ARPES
Layered: Possible High IPS-bulk coupling due to the presence of the Interlayer (IL) band
Ph.D Thesis defense Brescia, 11 January 2010
Graphite
IPS ON GRAPHITE
ZERO QUANTUM DEFECT – 40 fs LIFETIME FOR n=1 IPS
VANISHING QUANTUM DEFECT DUE TO THE PRESENCE OF THE INTERLAYER STATE
NEARLY-DEGENERATE WITH IPS
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative exciatations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Our method: NL-ARPES
INTENSE VIS / NEAR-UV LASER PULSES AS PROBE: MULTIPHOTON TRANSITIONS (hv < ) ACCESS TO EMPTY & EXCITED STATES
NON-LINEAR PHOTOEMISSION SPECTROSCOPY
Fauster 2003
TIME RESOLVED STUDIES
ACCESS to LIFETIMES
ABOVE TRESHOLD PHOTOEMISSION IN SOLIDS CONFIRMED USING 3.14 eV PULSES
Banfi et al. PRL 94, 037601 (2005)
1st PHOTON
2st PHOTON
OUR REALIZATION: va=vb
SINGLE PULSE MODE
Ph.D Thesis defense Brescia, 11 January 2010
Our method: NL-ARPES
OP
A
NO
PA
LEEDToF
3-4.2 eV 3-5 eV
UHV chamber
Energy density on sample: 1-2 J cm-2
3.14eV
SHGFHG
SHGSHG
Regenerative Amplifier
Ti:Sa oscillator
500nm cont.
50
0nm
1 K
hz
1 KHz 1 mJ =1.57 eV
76 MHz 10 nJ
Laser system
BS
f
sample
M
Light conversion stage
OP
A
NO
PA
LEEDToF
3-4.2 eV 3-5 eV
UHV chamber
Energy density on sample: 1-2 J cm-2
3.14eV
SHGFHG
SHGSHG
Regenerative Amplifier
Ti:Sa oscillator
500nm cont.
50
0nm
1 K
hz
1 KHz 1 mJ =1.57 eV
76 MHz 10 nJ
Laser system
SHG
Regenerative Amplifier
Ti:Sa oscillator
500nm cont.
50
0nm
1 K
hz
1 KHz 1 mJ =1.57 eV
76 MHz 10 nJ
Laser system
BS
f
sample
f
sample
M
Light conversion stage
NL-ARPES EXPERIMENTAL SETUP
120 fs; 1 KHz Rep. Rate ћ=3 – 5 eV ; F~100 μJ cm-2
ToF PARAM : Acc. Angle : 0.83° E = 30meV @ 2 eV EK
ToF
e-
θ
HOPG
P < 2 10-10 mbar, T=300 K
ACCESS TO THREE IPS QUANTITIES : IPS PE YIELD - IPS LINEWIDTH - IPS EFFECTIVE MASS
High intensity (>GW cm-2), Spatially coherent light pulses Pulse duration (120fs) << π* excitation lifetime (ps)
Ph.D Thesis defense Brescia, 11 January 2010
Our method: NL-ARPES
THREE POSSIBLE EXPERIMENTAL GEOMETRIES: A-B-C
A θ=30° =0
B θ=-40° =0
C θ=0° =45°
θ
ToF
Manip Axis
HOPG
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Normal Emission spectra
POLARIZATION SELECTION RULES
TWO FEATURES : IPS AND BULK π* SHOULDER
NORMAL EMISSION SPECTRA (A geom)
IPS QUANTUM DEFECT
22 )2()1(16
aaRy
E
04.008.0 a
IPS photoemitted only by e
π () photoemitted by e (e||)
SHIFT WITH PHOTON ENERGY
)(cos)( 2ppI
ћ=3.14 eV
Ph.D Thesis defense Brescia, 11 January 2010
TWO BULK EXCITATION REGIMES
TWO IPS POPULATION PROCESSES
MULTIPHOTON TRANSITIONS for IPS AND π*
Normal Emission spectra
MPO=2+1 = 3
MPO=1+1 = 2
OUT OF RESONANCE
IN RESONANCE
With π, π* SADDLE
IPS IS POPULATED IN A NO-RESONANT WAY BY SCATTERING OF THEHIGH DENSITY OF EXCITED ELECTRONS IN π* BANDS
Multi Photon Order
n~1020 cm-3 @ F=100 J cm-2
Ph.D Thesis defense Brescia, 11 January 2010
VARYING PHOTON ENERGY: STRUCTURE in IPS and π*
Normal Emission spectra
USING OPA – NOPA TO SPAN PHOTON ENERGY IN THE 3.2 – 4.2 RANGE
LINEAR IPS PHOTOEMISSIONRESONANT π π* vacuum
HOW ABOUT π* INTENSITY AND WIDTH?
MPO TRANSITION @ 4 eV
Electrons
Holes
4.0
-4.0
0.0
π
π*IPS
Ph.D Thesis defense Brescia, 11 January 2010
PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE
no π* FEATURE in 3.52 eV spectrumUsed as reference for secondary emission
Phot
oem
issio
n in
tens
ity (a
.u. –
linea
r sca
le) π* shoulder feature changes shape
And intensity with incident photon energy
SHOULDER EXTRACTION FROM DATA
Subtract the (shifted-normalized) 3.52 eV spectrum from raw data: difference
The π* FEATURE spectrum is fitted with a Fermi-Dirac function
Normal Emission spectra
Ph.D Thesis defense Brescia, 11 January 2010
PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE
NON-PERTURBATIVE REGIME
PERTURBATIVE REGIME
π* does not change with KE
π* changes with KE
3.60 < hv < 3.90
3.90 < hv < 4.15
Normal Emission spectra
SADDLE POINTEXCITATION
OFF-RESONANCEEXCITATION
1/1)(
WEeAEf
Int. Width
INCREASE in WidthINCREASE in Teff
2160 K
3120 K
THE IPS is populated by THE SAME π* ELECTRONS
Ph.D Thesis defense Brescia, 11 January 2010
Normal Emission spectra
IPS YIELD AND LINEWIDTH vs. ћ
PEAK IN THE IPS YIELD
STEP IN THE IPS FWHM of 60 meV
AT ћ=4.0 eVn()
3.6 4.0 4.4 4.8
INTENSITY INCREASE : EXPLAINED BY OPTICAL ABSORPTION + MPO CHANGE
BUT: 0.4 eV SHIFT : BANDGAP RENORMALIZATION
IPS LINEWIDTH STEP: CHANGE IN LIFETIME?
HIGH IPS INTERACTION WITH BULK EXCITATIONS
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
ANGLE RESOLVED SPECTRA: IPS EFFECTIVE MASS
The IPS dispersion has been measured for the first time in HOPG
*2)(
2||
2
0|| m
kEkEK
WE FOUND THAT m* DEPENDS on PHOTON ENERGY ћ
Maximum of m* @ 4.0 eV
IPS MASS RENORMALIZATION on HOPG
COULD BE INDUCED BY THE TRANSIENT OPTICAL EXCITATION in π BANDS
2DFEG
C GEOMETRY
Angle resolved spectra
Ph.D Thesis defense Brescia, 11 January 2010
k
0H )(0 H
ANSATZ:
FITTING PARAMETERS
')'(' kkk gd
ROUGH, “SELF-ENERGY” APPROACH
n()
ELECTRON POLARIZATION INTERACTION with IPS
vHs
0 50 fs 200 ? fs
e-EXCITATION
Hot e-
t
N(ω
) x 1
020 c
m-3
Photon energy
At k=0 USING KRAMERS-KRONIG RELATIONS:
?
Angle resolved spectra
Primitive cell density
Ph.D Thesis defense Brescia, 11 January 2010
IPS FWHMIPS EFFECTIVE MASS
vHs
FITTING RESULTSPrevious results allows us to fit C-geometry (symmetric) measurements without further analysis
IPS effective mass AND linewidth behaviour are linked by the model.
PEAK / STEP IN CORRESPONDENCE OF THE RENORMALIZED VAN HOVE SINGULARITY
Angle resolved spectra
Ph.D Thesis defense Brescia, 11 January 2010
Angle resolved spectra
GEOMETRY-DEPENDENT SYMMETRY OF IPS DISPERSION
HIGHER PHOTON ENERGY REQUIRES SYMMETRIC GEOMETRY!
A A
B C+
Ph.D Thesis defense Brescia, 11 January 2010
Angle resolved spectra
Θmp-DEP. OF PARALLEL POLARIZATION FLUENCE
GEOMETRIC EFFECT (SPOT SIZE) + FRESNEL EFFECT (FIELD PROJECTION)
Ph.D Thesis defense Brescia, 11 January 2010
GEOMETRY-DEPENDENT ASYMMETRY EXPLAINED
)1()( 0, akFkF BA
20 21)( kb
FkF C
A and B geometry C geometry
A
IF ||
Fresnel
Geometric projection
Rotating Frame:
Varying θ varying F varying m*=m*(k)
m* NEARLY CONSTANT for LOW ε2 and/or C geometry :
3.14 eV 3.93 eV
A
B
A
C
Angle resolved spectra
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
Model calculations
* TRANSITION : LASER-INDUCED CORRUGATION AT THE SURFACE
Modifications to the effective mass due to the 1-body IPS interaction with the corrugation potential
Ground state IPS
Periodic corrugation pot. V2nd order perturbation th.
Effective mass at (orientational average)
Ph.D Thesis defense Brescia, 11 January 2010
x (aB)
y (aB )
ρ(x,y)
Model calculations
SPATIAL PART OF THE CORRUGATION CHARGE: TIGHT BINDING MODEL
Wannier functions of the bands
Excited carrier densityn
T
TTNk
krkrr2
*
2),(),()(),( Periodic
Ph.D Thesis defense Brescia, 11 January 2010
PREDICTION: Δm/m () ≈ 10-4
n≈1020 cm-3 @ F=100 J cm-2
Model calculations
IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS
INN(1,1)
Dominant terms: G=NN, n=1
)]1,1(2)1,1([116
1/* 2142
2
NNNNNN
IIG
mmm
Ph.D Thesis defense Brescia, 11 January 2010
Outline
THESIS OUTLINE
1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS
4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations
7. Model calculations: Photoinduced polarization
8. Conclusions
Ph.D Thesis defense Brescia, 11 January 2010
LW
m*
IPS IN GRAPHITE IS SENSIBLE TO LASER
INDUCED POLARIZATION
n()
5. Role of LAYERED HOPG +HIGH-I LASER PULSES
Conclusions
3. Important PHOTOINDUCED modifications of IPS dispersion
4. Evidence of a PHOTOINDUCED * excitations - IPS INTERACTION ( * SADDLE POINT)
1. Image Potential States on HOPG studied by NL-ARPES
FUTURE/2 MEASUREMENTS: TR-ARPES with ToF2D
FUTURE/1 COMPUTATIONAL WORK to confirm the coupling dynamics
2. PE YELD – LineWidth – Effective mass measured
EXPLORING EXCITED STATE STRUCTURE BY NL-ARPES &
SURFACE IPS!
Ph.D Thesis defense Brescia, 11 January 2010
ELPHOS Lab: Who
Fulvio Parmigiani
Stefania Pagliara
Gabriele Ferrini
Gianluca Galimberti
Stefano dal Conte
RESEARCH STAFF
Ph.D Thesis defense Brescia, 11 January 2010
THANK YOU.
Ph.D Thesis defense Brescia, 11 January 2010
Milano
BRESCIA
Roma
ELPHOS Lab: Where
Ph.D Thesis defense Brescia, 11 January 2010
Photoinduced polarization
* TRANSITION : LASER-INDUCED POLARIZATION
T
TTNk
krkrr2
*
2),(),()(),( )()( 2 d
c
FN
AT 4 eV: MAXIMUM DENSITY
Laser pulse induces a strong charge polarization at the surface. Strenght depends on ћ
F = pulse fluence (J cm-2)
TIGHT BINDING + Nearly Free Electron Model(quite a message...)
IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS
BGR
2NDNN
Ph.D Thesis defense Brescia, 11 January 2010
Ph.D Thesis defense Brescia, 11 January 2010
Moos PRL 87, 267402 (2001)
Ph.D Thesis defense Brescia, 11 January 2010
Normal Emission spectra
IPS INTENSITY AND LINEWIDTH MEASUREMENTS
RESONANCE IN IPS INTENSITY STEP IN IPS LINEWIDTH
Ph.D Thesis defense Brescia, 11 January 2010
PHONONS DISPERSION OF GRAPHTE
Mohr PRB 76, 035439
Ph.D Thesis defense Brescia, 11 January 2010
BAND SADDLE POINT
EVIDENCE OF HIGH COUPLING of
ELECTRONS with PHONONS or DEFECTS
πM
Moos PRL 87, 267402 (2001)
Zhou, PRB 71, 161403(R) (2005)
Graphite
ANOMALY in QUASIPARTICLE LIFETIMES due to DISPERSION
DIELECTRIC FUNCTION
Taft, PR 138, A197 (1964)
Ph.D Thesis defense Brescia, 11 January 2010
BAND SADDLE POINT
THE , * SADDLE POINT is a PECULIAR point for the excited dynamics in graphite
- IMPORTANT DEVIATIONS from the FERMI LIQUID BEHAVIOUR of excitations
Plateau in the QP relaxation lifetimeTime-resolved photoemission -> QP lifetimes
Energy- and momentum- conservation hamper decay of M point excitations
Moos PRL 87, 267402 (2001)
Graphite
Ph.D Thesis defense Brescia, 11 January 2010
Posternak, PRL 52, 863(1984)In HOPG the IPS is the surface state of the INTERLAYER (IL) BAND
Bulk Vacuumn=1
IPS
IL
z
x
U(z)
IPS OVERLAPS WITH THE IL BAND = CHANNEL TO HIGHER IPS-BULK COUPLING
1D Periodicity (Kronig-Penney)
Pseudo-Rydberg IPS
1
)()();();(2
nnnzz
k
z zzdkkzkzL
z
1
IL band
IPS employed as a probe to the bulk to solve the IL band position controversy
IS IPS MORE SENSIBLE TO PHOTO-INDUCED POLARIZATIONS?
Graphite
Lehman PRB 60, 17 037 (1999)
Photoinduced PolarizationHigh IL(bulk)- IPS coupling
θe-
THE IPS AND THE INTERLAYER STATE
Ph.D Thesis defense Brescia, 11 January 2010
Our method: NL-ARPES
Time of Flight (ToF) detector employedto measure electron kinetic energies.
EK=1/2 mev2 v= L/Δt
Scattering from sample used to set zero-time referenceEffective ToF lenght L determined by characterization
OPTIMAL for SHORT-PULSE LASER SOURCES
TIME OF FLIGHT DETECTION SCHEME
CONTACT POTENTIAL
L
KE corrected for CONTACT POTENTIAL
SAMPLE WORK FUNCTION MEASURED =4.50 ±0.1eV
With hv=6.28 eV