Vanishing Spin-Hall Conductivity in 2D disordered Rashba electron gas

TL;DR

This paper demonstrates through microscopic calculations that the spin-Hall conductivity in a 2D disordered Rashba electron gas vanishes under typical semiclassical conditions, regardless of the ratio of spin-orbit splitting to scattering rate.

Contribution

It provides a direct microscopic proof that the spin-Hall conductivity is zero in a disordered 2D Rashba system within the semiclassical approximation.

Findings

Spin-Hall conductivity is zero under semiclassical conditions.

The result holds for any ratio of spin-orbit splitting to scattering rate.

Abstract

For the two-dimensional ideal electron gas with the Rashba spin-orbit interaction and in the presence of non-magnetic short-ranged potential impurities the spin-Hall conductivity $\sigma_{sH}$ is found by direct microscopic calculation. Within the semiclassical approximation $\hbar/\tau \ll \epsilon_F$ and $\Delta \ll \epsilon_F$ the value of $\sigma_{sH}$ is zero for arbitrary ratio of the spin-orbit splitting $\Delta$ and the inverse elastic scattering time $1/\tau$.