Onsager Relations in Coupled Electric, Thermoelectric and Spin Transport: The Ten-Fold Way

TL;DR

This paper develops a comprehensive quantum scattering theory for coupled electric, heat, and spin transport, deriving Onsager reciprocity relations across all ten symmetry classes, including effects involving superconductors and spin caloritronics.

Contribution

It provides a complete classification of Onsager relations for coupled transport in all ten symmetry classes, incorporating effects like Andreev reflection and spin caloritronics.

Findings

Reciprocity between spin-Hall and inverse spin-Hall effects

Relations between spin-injection and magnetoelectric spin currents

Symmetry-based Onsager relations for thermoelectric effects

Abstract

Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of time-reversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to specific additional relations that follow from the combination of symmetries, beyond microreversibility. We discuss these relations in several illustrative situations. We show the reciprocity between spin-Hall and inverse spin-Hall effects, and the reciprocity between spin-injection and magnetoelectric spin currents. We discuss the symmetry and reciprocity relations of Seebeck, Peltier, spin-Seebeck and spin-Peltier effects in systems with and without coupling to superconductors.