Spin caloritronics with superconductors: Enhanced thermoelectric effects, generalized Onsager response-matrix, and thermal spin currents

Abstract

It has recently been proposed and experimentally demonstrated that it is possible to generate large thermoelectric effects in ferromagnet/superconductor structures due to a spin-dependent particle-hole asymmetry. Here, we show theoretically that quasiparticle tunneling between two spin-split superconductors enhances the thermoelectric response manyfold compared to when only one such superconductor is used, generating Seebeck coefficients ($\mathcal{S}>1$ mV/K) and figures of merit ($ZT\ensuremath{\simeq}40$) far exceeding the best bulk thermoelectric materials, and it also becomes more resilient toward inelastic-scattering processes. We present a generalized Onsager response-matrix that takes into account spin-dependent voltage and temperature gradients. Moreover, we show that thermally induced spin currents created in such junctions, even in the absence of a polarized tunneling barrier, also become largest in the case in which spin-dependent particle-hole asymmetry exists on both sides of the barrier. We determine how these thermal spin-currents can be tuned both in magnitude and sign by several parameters, including the external field, the temperature, and the superconducting phase difference.