Spin-dependent thermoelectric phenomena in a quantum dot attached to ferromagnetic and superconducting electrodes

Abstract

We investigate transport and thermoelectric properties of hybrid systems based on a single-level quantum dot and one superconducting lead. The other lead is generally normal-metallic ferromagnet. In the latter case single-particle transport is spin-polarized. Our main interest is in the interplay of Andreev tunneling of Cooper pairs and single-particle tunneling. The latter is responsible for relatively large thermopower and figure of merit due to a diverging density of single-particle states at the superconducting gap edges. System with ferromagnetic and superconducting leads can also reveal spin thermoelectric phenomena. Finite superconducting gap is considered within the BCS theory, and the thermoelectric coefficients are calculated by means of nonequilibrium Green's function technique within Hartree-Fock like approximation with respect to the intradot Coulomb interaction.

Thermopower and thermal conductance of a superconducting quantum point contact

“…Here we only mention several noteworthy observations evident from Eq. (19). 36 The first two terms in the square brackets of the integrand of Eq.…”

“…36 The first two terms in the square brackets of the integrand of Eq. (19) give the leading terms in the asymptotic behavior of g SS T (ϕ, ∆/T, τ ) at ϕ → 0 or at ∆/T → 0. The leading asymptote at ∆/T → 0 and fixed ϕ is…”

“…The second modification is the need of an overall factor 1/2 in Eq. (19) reflecting the absence of spin degeneracy for a helical channel. These two modifications indeed reduce Eq.…”

“…The existing theory of thermally-induced charge and entropy currents through weak links employs the tunneling Hamiltonian approximation in considering superconductor-insulator-superconductor (SIS) junctions [9,10,17] or more complex structures [18,19]. Other approaches use semiclassical description of diffusive [20,21] or ballistic [12,13] weak links or junctions be-tween a normal-state material and superconductor (NS junction).…”

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

“…Unfortunately, particle-hole symmetry is generally preserved in a superconductor and this leads to a perfect cancellation of the thermoelectric current due to counterpropagating electron and hole flows. The symmetry can be broken with external magnetic fields or spin-polarized bands [18], leading to sizable values of S as demonstrated both theoretically [19,20,21,22,23,24,25,26,27,28] and experimentally [29,30]. Another possibility is to drive the junction out of equilibrium beyond the linear response regime.…”