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.