Off-Fermi surface cancellation effects in spin-Hall conductivity of a two-dimensional Rashba electron gas

TL;DR

This paper investigates how vertex corrections affect the spin-Hall conductivity in a disordered 2D Rashba electron gas, revealing that at low electron densities, off-Fermi surface contributions dominate and prevent suppression of the spin current.

Contribution

It demonstrates that off-Fermi surface effects become significant at low electron densities, altering the understanding of spin-Hall conductivity suppression in Rashba systems.

Findings

Vertex corrections suppress spin-Hall conductivity at high electron densities.

Off-Fermi surface contributions dominate at low densities, preventing suppression.

Spin current persists due to off-Fermi surface effects when $E_F \\lesssim E_0$.

Abstract

We calculate the spin-Hall conductivity of a disordered two-dimensional Rashba electron gas within the self-consistent Born approximation and for arbitrary values of the electron density, parametrized by the ratio $E_F /E_0$, where $E_F$ is the Fermi level and $E_0$ is the spin-orbit energy. We confirm earlier results indicating that in the limit $E_F/E_0 \gg 1$ the vertex corrections suppress the spin-Hall conductivity. However, for sufficiently low electron density such that $E_F\lesssim E_0$, we find that the vertex corrections no longer cancel contributions from the Fermi surface, and they cannot therefore suppress the spin current. This is instead achieved by contributions away from the Fermi surface, disregarded in earlier studies, which become large when $E_F\lesssim E_0$.