Explorations in quantum transport – phenomena and methods...
Transcript of Explorations in quantum transport – phenomena and methods...
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Explorations in quantum transport –phenomena and methods
Sokrates T. Pantelides Department of Physics and astronomy, Vanderbilt University, Nashville, TN
andOak Ridge National Laboratory, Oak Ridge, TN
Collaborators: Yoshihiro GohdaZhong-yi LuKalman Varga
Supported in part by Department of Energy
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MOORE’S LAW
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• Phenomena (using the Lippmann-Schwinger method)
• Charging of molecules during transport (Gohda)
• Transport through ultra-thin films (Lu)
• New method (Varga)
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The Lippmann-Schwinger method
• Norton Lang, 1981 –
t
r
• Di Ventra, Lang, and Pantelides, 2000-2002
Ψ+Ψ=Ψ VG00
{0 ,
ik z ik zr r
ik zl
e re z
te z
−
−+ →+∞
→−∞Ψ ∝
� Ψ∇Ψ−=FR
FL
E
E
rrdErJ )]()(Im[2)( *
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Experiment: Reed et al (2000)
T=190 K T=300 K
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Theory
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Nature 417, 72 (2002)
“The current is strongly suppressed up to a threshold V, then it increases in steps”
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Coulomb blockade in a quantum dot
GaAs-AlGaAs-InGaAs-AlGaAs-GaAs
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Barner and Ruggiero, 1987
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V=2.4V
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AFTER SELF-CONSISTENCY,
MOLECULE IS NEUTRAL!
ELECTRODES ARE NEUTRAL!
EXCITED STATE?
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C6H5S
ELIMINATE CONTACT ON LEFT
C6H4(NO2)S
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-6 -4 -2 0 2
Energy (eV)
C6H5-S C6H4(NO2)-S
Energy (eV)
-3 -2 -1 0 1
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0.6V0 e
1.8V1 e
4.2V1 e
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Vsd = 0.1 V
Using a gate voltage
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n-Si
MetalSiO2
EF
Ec
Ev
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I=V/R
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8-layer Si(001)
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The dash-dot lines are boundary
EF
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V=5.0v
V=1.0v
V=0.1v
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Three regions:(1) 0.0 to 0.5V quasi-linear;(2) 0.5 to 4.0V non-linear;(3) Over 4.0V quasi-linear
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The dash-dot lines are boundary
EF
SiO2
V= 4.0v
nano-film
V=0.5v
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1.2 n m (SiO 2)
1.5 n m (SiO2)
0.9 n m (vacuum)
1.2 n m (vacuum)
1.5 n m (vacuum)
0 1 2 3 4 5
G. Timp et al (Bell Lab) 1998 calculation
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The Lippmann-Schwinger method
t
r
Ψ+Ψ=Ψ VG00
{0 ,
ik z ik zr r
ik zl
e re z
te z
−
−+ →+∞
→−∞Ψ ∝
� Ψ∇Ψ−=FR
FL
E
E
rrdErJ )]()(Im[2)( *
0∇ ⋅ =J EVERYWHERE
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DENSITY FUNCTIONAL THEORYFOR STEADY-STATE TRANSPORT
(CURRENT-DENSITY FUNCTIONAL)
[ ] [ ] 0 0E J E J Aαα α αδ = ∂ =21
2{ ( ) }xc ext H xcH i V V Vψ ψ εψ= − ∇ + + + + + =A A
Static external potential ( )extV x + B.C.
( )xcρ= + +J j A A *Im ( )ψ
ψ ψ= − ∇�j
2HV ρ∇ = − 2 ( ) 0∇ − ∇ ∇ ⋅ = − ∇ ⋅ =A A J J
*
ψρ ψ ψ=�
[ , ]xc
EV
δ ρδρ
= J [ , ]xc
Eδ ρδ
= JA
J
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2W ( ) ))2
IW x L x Rρ δ δ
ρ∇ ⋅ = = ( − − ( −J
( )H iW ψ εψ+ =
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Source Sink
Battery!
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Na wire
0.0 0.5 1.0 1.5 2.0Bias Voltage (V)
0.00
0.02
0.04
0.06
0.08
0.10
Cur
rent
(m
A)
Real-space DFT calculationJellium electrodesBias Voltage
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Experiment
(Reed et al.)
Benzene ring -- IV characteristics