Spin-Hall effect in a disordered 2D electron-system

TL;DR

This paper investigates the spin-Hall effect in a disordered 2D electron system, revealing that the total spin-Hall conductivity cancels out in the weak disorder limit due to the interplay of reactive and dissipative responses.

Contribution

It provides a detailed calculation of spin-Hall conductivity considering disorder effects, showing the universal reactive response cancels with the dissipative part in the weak disorder limit.

Findings

Reactive spin-Hall response is universal at e/8π.

Dissipative response cancels the reactive response.

Total spin-Hall conductivity vanishes in the weak disorder limit.

Abstract

We calculate the spin-Hall conductivity for a two-dimensional electron gas within the self-consistent Born approximation, varying the strength and type of disorder. In the weak disorder limit we find both analytically and numerically a vanishing spin-Hall conductivity even when we allow a momentum dependent scattering. Separating the reactive from the disspative current response, we find the universal value $\sigma^R_{sH} = e/8 \pi$ for the reactive response, which cancels however with the dissipative part $\sigma^D_{sH} = -e/8 \pi$.