Transport properties: conductance and thermopower

Rok ŽitkoInstitute Jožef StefanLjubljana, 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

One impurity:

Also known as the Meir-Wingreen formula

Relection symmetric problems:

Conductance of quantum dot (SIAM)

Finite temperatures

Effect of the magnetic field

A B

V~0

A B

V>0

I

V

dI/dV

V

A B

V~0

A B

eV>hw

I

V

dI/dV

Vħw

ħw

ħw

Inelastic scattering

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

Spin thermopower is a sensitive probe of the response of the system in magnetic field.

Žitko, Mravlje, Ramšak, Rejec,

manuscriptin preparation.