Microscopic theory of spin Nernst effect

TL;DR

This paper develops a microscopic, thermodynamically consistent theory for the spin Nernst effect in non-interacting electron systems, deriving formulas linking spin Nernst and spin Hall effects, and demonstrating results for Dirac electrons.

Contribution

It introduces a comprehensive microscopic framework for the spin Nernst effect, including derivations of Mott's and Středa formulas for spin currents, applicable to non-interacting and potentially interacting systems.

Findings

Derived the spin-current Mott's formula relating spin Nernst and spin Hall conductivities.

Ensured the theory's consistency with thermodynamics and low-temperature behavior.

Calculated the spin Nernst current for three-dimensional Dirac electrons.

Abstract

We present the microscopic theory of the spin Nernst effect, which is a transverse spin current directly induced by a temperature gradient, employing the linear response theory with Luttinger's gravitational potential method. We consider a generic, non-interacting electron system with randomly distributed impurities and evaluate the spin current response to the gravitational potential. Our theory takes into account a contribution of the local equilibrium current modified by Luttinger's gravitational potential and is thus consistent with the thermodynamic principle that thermal responses should vanish. The Ward-Takahashi identities ensure that the spin Nernst current is well-behaved at low temperatures in any order of the random impurity potentials. Furthermore, we microscopically derive the spin-current version of Mott's formula, which associates the spin Nernst coefficient with the spin Hall conductivity. The spin-current version of the St\v{r}eda formula is also discussed. To demonstrate these findings, the spin Nernst current of three-dimensional Dirac electrons is computed. Our theory is general and can therefore be extended to interacting electron systems, where Mott's formula no longer holds.