Conserved spin current for the Mott relation

TL;DR

This paper demonstrates that the conserved spin current satisfies the Mott relation linking the spin Hall effect and the spin Nernst effect, with a sign change observed in a specific 2D system.

Contribution

It reveals that the conserved spin current obeys the Mott relation, connecting spin Hall and spin Nernst effects, which was not previously established.

Findings

The conserved spin current automatically satisfies the Onsager relation.

The spin Nernst conductivity can change sign when tuning the chemical potential.

The study focuses on a 2D Dirac-Rashba system with scalar disorder.

Abstract

The conserved bulk spin current [Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], defined as the time derivative of the spin displacement operator, ensures automatically the Onsager relation between the spin Hall effect (SHE) and the inverse SHE. Here, we reveal another desirable property of this conserved spin current: the Mott relation linking the SHE and its thermal counterpart, the spin Nernst effect (SNE). According to the Mott relation, the SNE is known once the SHE is understood. In a two-dimensional Dirac-Rashba system with a smooth scalar disorder potential, we find a sign change of the spin Nernst conductivity when tuning the chemical potential.