magnetopolaronic effects in single-molecule transistor
DESCRIPTION
Magnetopolaronic effects in single-molecule transistor. I.V.Krive, S.I.Kulinich, G.A.Skorobagatko M.Jonson and R.I.Shekhter. - B.Verkin ILTPE of NAS of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine -University of Gothenburg, SE-412 96 Gothenburg, Sweden. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/1.jpg)
Magnetopolaronic effects Magnetopolaronic effects in single-molecule in single-molecule transistortransistor
![Page 2: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/2.jpg)
““Magnetopolaronic Effects in Electron Transport Magnetopolaronic Effects in Electron Transport through a Single-Level Vibrating Quantum Dot” , through a Single-Level Vibrating Quantum Dot” , FizikaFizika Nizkikh Temperatur, Vol.37, 12, (December 2011), Nizkikh Temperatur, Vol.37, 12, (December 2011), pp. 1295-1301.pp. 1295-1301.
I.V.Krive, S.I.Kulinich, I.V.Krive, S.I.Kulinich, G.A.SkorobagatkoG.A.Skorobagatko
M.Jonson and M.Jonson and R.I.ShekhterR.I.Shekhter
- B.Verkin ILTPE of NAS - B.Verkin ILTPE of NAS of Ukraine, 47 Lenin of Ukraine, 47 Lenin Ave., Kharkov 61103, Ave., Kharkov 61103, UkraineUkraine
-University of -University of Gothenburg, SE-412 96 Gothenburg, SE-412 96 Gothenburg, SwedenGothenburg, Sweden
![Page 3: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/3.jpg)
Plan.Plan.
Single-molecule transistors (experiment).Single-molecule transistors (experiment).
Vibrational effects: vibron-assisted tunneling, electron Vibrational effects: vibron-assisted tunneling, electron shuttling, polaronic blockade.shuttling, polaronic blockade.
Magnetic field-induced electromechanical coupling.Magnetic field-induced electromechanical coupling.
Magnetopolaronic effects in sequential and resonant Magnetopolaronic effects in sequential and resonant electron transport.electron transport.
![Page 4: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/4.jpg)
Single Molecule Transistor
C60 in vacuum
eV 4.76-LUMO
eV 6.40-HOMO
eVEE HL 6.1
eVCEL 8.1)( 60
eVdeCECEF
LL 3)()(2
6060
Low-T characteristics of SMT(i) Coulomb blockade(ii) Conductance oscillations on VG (CBO)
![Page 5: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/5.jpg)
Nature, 407, 57, (2000)
Quantized nano-mechanical oscillations of the C60 against the gold electrode (ω~1.2 THz) result in additional steps (hω~5 μeV) in I-V curves.
![Page 6: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/6.jpg)
Nano letters, 5(2), p.203, (2005)
![Page 7: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/7.jpg)
Nanoelectromechanics of Suspended Carbon Nanotubes
First experiment: S Sapmaz et al., PRL, 96, 026801 (2006), H.van der Zant group, Kavli Institute of Nanoscience, Delf Univ. of Technology
Low-T electron transport:(i) T>>Г0 sequential electron tunneling(ii) T~Г0 resonant electron tunneling
Suspended SWNT<=>vibrating QD
Electron tunneling in the presence of VG is accompanied by the shift of c.m.c. of the nanotube towards back gate (tunneling induces mechanical vibrations of the nanotube)
I-V curve of nanotube-based SET (L~0.1-1 μm) revealed vibrational effects induced by stretching mode (~0.6 meV)
![Page 8: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/8.jpg)
Nanoelectromechanical Coupling in Fullerene Peapods
Theory: I.V. Krive, R. Ferone, R.I. Shekhter, M. Jonson, P. Utko, J. Nygard, New J. Phys. 10, 043043 (2008)
Experiment: P. Utko, R. Ferone, I.V. Krive, R.I. Shekhter, M. Jonson, M. Monthioux, L. Noe, J. Nygard, Nature Com. 1, 37 (2010)
Empty SWNT
“peapod”
– mechanical frequency of cluster oscillations
– dimensionless electromechanical coupling
– Bose distribution function
,, gBWg VGfdTVG T TG m 1~
Tz /0 0
n
l
l
lzznznIlz
znzF2/cosh
122/exp21exp 2
22
zFGG mm
![Page 9: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/9.jpg)
Experimental Results
![Page 10: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/10.jpg)
Vibron-assisted tunneling
“Toy” model (Holstein) tunQDleads HHHH
)(,)(,
pkaaaaH jmRLj
pkkkjkleads mjjjj
0 0 int1( ) , ( ), ( )2 2QD
iH c c b b b b c c x b b p b b
(0)
,
H.c., [ , ] 1, [ , ] 1jtun j k
k j
H t a c b b c c
Unitary transformation: ˆ ˆ ˆexp( ),H UHU U i pn n c c
bbccH pQD 0
~
H.c.~ )(0
)(
k
pik
jjt ecatH
j
20 0
int 02 /p
-polaronic shift
![Page 11: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/11.jpg)
Sequantial electron tunneling and polaron tunneling approximation
2. Non-monotonic (anomalous) T-dependence of conductance at (strong coupling) 0T
TTGe
2ch, 2-
00
2
0 0T
sequential tunneling
3. Vibron-assisted tunneling (weak or moderately strong coupling)
1. Polaronic (Franck-Condon) “blockade” (strong coupling)
![Page 12: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/12.jpg)
ˆ ( )cx x t
Nonlinear integral-differential equation for classical coordinate:
)(20 txFxx ccc
At eV>hω0 xc=0 is unstable solution
Electron Shuttling
0exp( / ), ( , ) ( , )j tt t jx j L R
,
( ) ( 1) Rej
jc j k
k j
HF n x t t a cx
First publication: L.Y.Gorelik et al., PRL, 80, 4526, (1998) Single level quantum dot: D.Fedorets et al., Europhys. Lett., 58 (1), pp. 99-104, (2002)
Cyclic (stable) solution ( ) sin( )cx t A t
![Page 13: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/13.jpg)
Nanomechanical Shuttling of Electrons
bias voltage dissipation
current
Theory:Gorelik, Shekhter et al, Phys. Rev. Lett., 1998Shekhter et al., J. Comp. Th. Nanosc., 2007
Experiment: H.S.Kim, H.Qin, R.Blick, arXiv:0708.1646A.V.Moskalenko et al.,Phys.Rev B79 (2009)J. Kotthaus et al, Nature Nanotechnology 2008
![Page 14: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/14.jpg)
Quantum Fluctuation-Induced Aharonov-Bohm Effect
B
2
0
0
20 0
0
411 , 1,6
41 1exp ,2
y LHkTG kT
G y LHkT
R.I. Shekhter, L.Y. Gorelik, L.I. Glazman, M. Jonson, PRL 95(11), 156801 (2006)
![Page 15: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/15.jpg)
Tunneling Transport in Magnetic Field.Tunneling Transport in Magnetic Field.
Hamiltonian
Single-level QD with single vibrational mode(bending mode for SWNT)
-is the tunneling length
-is the “size” of quantum dot
![Page 16: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/16.jpg)
Laplace and cohesive forces.Laplace and cohesive forces.
Heisenberg equations of motion:Heisenberg equations of motion: 2 equations for fermionic operators : ,2 equations for fermionic operators : , Equation for coordinate operator Equation for coordinate operator
Cohesive force:
Laplace force:
![Page 17: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/17.jpg)
Classical regime of vibrations: Classical regime of vibrations:
where:
and
with - Breit-Wigner transmission coefficient
- Fermi distribution function
![Page 18: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/18.jpg)
Quantum regime of vibrations.Quantum regime of vibrations.
Tunneling amplitude:
- is the dimensionless strength of electron-vibron coupling
I. Sequential tunneling:
Spectral weights
are defined by equation:
-noninteracting vibrons!
Equilibrium vibrons:
![Page 19: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/19.jpg)
Magnetopolaronic Blockade; Anomalous Magnetopolaronic Blockade; Anomalous Temperature Dependence ; Excess Temperature Dependence ; Excess
current.current.
Conductance:
Current:
Frank-Condon factors:
Excess current:
![Page 20: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/20.jpg)
Polaronic Effects in Resonant Electron Tunneling
Polaron tunneling approximation (PTA)
20t
te
~ 20
1~~
p
p
12
1,
1,
arpRPAar GG 2/Im , tar
n
np n
AG
00
RL
pt
pRL ffG
Gd
heJ
2
2
2/1
4/22
00
RLF
RLGG
RLj e ,
2
0 F
electron dwell time characteristic time of polaron formation
In this approximation
By making use of the Meir-Wingreen formula for the average current through interaction QD we get
No polaronic effects at resonance condition
polaron Green function
In particular at low temperatures resonant conductance
![Page 21: Magnetopolaronic effects in single-molecule transistor](https://reader036.vdocuments.net/reader036/viewer/2022081604/56815616550346895dc3d56a/html5/thumbnails/21.jpg)
ConclusionConclusion
In electron transport through a vibrating QD polaronic effects are the same for electric field or magnetic field-induced electromechanical coupling.
The manifestations of polaronic (Franck-Condon) blockade are: (i) anomalous temperature dependence of conductance at , and (ii) the excess current in J-V curves at low temperatures.
Magnetopolaronic effects are most pronounced in the regime of sequential electron tunneling. Resonant conductance is not renormalized by magnetic field
in polaron tunneling approximation.
T