Spin Hall and spin Nernst effects in a two-dimensional electron gas with Rashba spin-orbit interaction: temperature dependence

TL;DR

This paper analytically investigates how temperature affects spin Hall and spin Nernst conductivities in a 2D electron gas with Rashba interaction, highlighting the suppression of spin Hall conductivity by vertex corrections and the temperature-dependent behavior of spin Nernst conductivity.

Contribution

It provides analytical formulas for temperature-dependent spin conductivities and includes the orbital magnetization contribution, offering new insights into their behavior at finite temperatures.

Findings

Vertex correction suppresses spin Hall conductivity at all temperatures.

Spin Nernst conductivity vanishes at zero temperature when orbital magnetization is included.

Finite temperature induces nonzero spin Nernst conductivity, contrasting with zero-temperature behavior.

Abstract

Using the Matsubara Green function formalism we calculate the temperature dependence of spin Hall and spin Nernst conductivities of a two-dimensional electron gas with Rashba spin-orbit interaction in the linear response regime. In the case of spin Nernst effect we also include the contribution from spin-resolved orbital magnetization, which assures correct behavior of the spin Nernst conductivity in the zero-temperature limit. Analytical formulas for the spin Hall and spin Nernst conductivities are derived in some specific situations. Using the Ioffe-Regel localization criterion, we have also estimated the range of parameters where the calculated results for the spin Hall and spin Nernst conductivities are applicable. Analytical results show that the vertex correction totally suppresses the spin Hall conductivity at arbitrary temperature. The spin Nernst conductivity, in turn, vanishes at $T=0$ when the orbital contribution is taken into account, but generally is nonzero at finite temperatures.