Difficulty - NRG Ljubljana

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Transport properties:
conductance and thermopower
Rok Žitko
Institute Jožef Stefan
Ljubljana, Slovenia
Transport in nanostructures
Landauer formalism
Density of states per unit length:
(Includes factor 2 for spin)
For T(E)=1 (ballistic conductor):
In general, at T=0:
Multi-channel leads:
resistance
quantized contact resistance
Scattering theory
quasiparticle phase shifts
Spin symmetry, single effective channel:
Keldysh approach
Relection symmetric problems:
One impurity:
Also known as the Meir-Wingreen formula
Conductance of quantum dot (SIAM)
Finite temperatures
Effect of the magnetic field
A
B
A
V~0
B
V>0
I
dI/dV
V
V
A
B
A
B
ħw
eV>hw
V~0
Inelastic scattering
I
dI/dV
ħw
ħw
V
V
Information about internal degrees of freedom!
Linear response theory for calculating the conductance
of nanostructures
Kubo (1957)
Standard approach:
Difficulty: the slope is difficult to calculate reliably!
Solution: we can work with the global operator Nn itself!
Test case: single-impurity Anderson model
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?
Transport integrals, thermopower
B=0
d=0 (particle-hole symmetric point)
(charge) Seebeck coefficient
spin Seebeck coefficient
Žitko, Mravlje,
Ramšak, Rejec,
manuscript
in preparation.
Spin thermopower is a sensitive probe of the response of the system in magnetic field.

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