Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana,...
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Transcript of Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana,...
![Page 1: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/1.jpg)
Transport properties: conductance and thermopower
Rok ŽitkoInstitute Jožef StefanLjubljana, Slovenia
![Page 2: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/2.jpg)
Transport in nanostructures
![Page 3: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/3.jpg)
Landauer formalism
![Page 4: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/4.jpg)
Density of states per unit length:
(Includes factor 2 for spin)
![Page 5: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/5.jpg)
For T(E)=1 (ballistic conductor):
In general, at T=0:
Multi-channel leads:
resistance
quantized contact resistance
![Page 6: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/6.jpg)
Scattering theory
quasiparticle phase shifts
Spin symmetry, single effective channel:
![Page 7: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/7.jpg)
Keldysh approach
One impurity:
Also known as the Meir-Wingreen formula
Relection symmetric problems:
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Conductance of quantum dot (SIAM)
![Page 9: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/9.jpg)
![Page 10: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/10.jpg)
Finite temperatures
![Page 11: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/11.jpg)
Effect of the magnetic field
![Page 12: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/12.jpg)
A B
V~0
A B
V>0
I
V
dI/dV
V
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A B
V~0
A B
eV>hw
I
V
dI/dV
Vħw
ħw
ħw
Inelastic scattering
Information about internal degrees of freedom!
![Page 14: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/14.jpg)
Linear response theory for calculating the conductance of nanostructures
Kubo (1957)
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Standard approach:
Difficulty: the slope is difficult to calculate reliably!
Solution: we can work with the global operator Nn itself!
![Page 16: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/16.jpg)
Test case: single-impurity Anderson model
![Page 17: Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia.](https://reader030.fdocuments.in/reader030/viewer/2022033104/56649e4f5503460f94b46c93/html5/thumbnails/17.jpg)
Proposed application:conductance of a S-QD-N structure
• Open problem: the transition from G=4e2/h to G=2e2/h conductance as the gap closes
1) 2)
3) 4)
Anyone interested?
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Transport integrals, thermopower
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B=0 d=0 (particle-hole symmetric point)
(charge) Seebeck coefficient spin Seebeck coefficient
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Spin thermopower is a sensitive probe of the response of the system in magnetic field.
Žitko, Mravlje, Ramšak, Rejec,
manuscriptin preparation.