Spin-Hall effect in a [110] quantum well

TL;DR

This paper provides a comprehensive theoretical analysis of the spin-Hall effect in a [110] GaAs quantum well, incorporating spin-orbit coupling, impurity scattering, and electron interactions to accurately calculate the spin-Hall conductivity.

Contribution

It introduces a self-consistent, exact linear response framework that includes Dresselhaus terms and distinguishes skew-scattering from side-jump contributions.

Findings

Spin-Hall conductivity separates into skew-scattering and side-jump contributions.

Theoretical predictions include effects of Dresselhaus linear and cubic terms.

Proposes an experiment to differentiate between skew-scattering and side-jump mechanisms.

Abstract

A self-consistent treatment of the spin-Hall effect requires consideration of the spin-orbit coupling and electron-impurity scattering on equal footing. This is done here for the experimentally relevant case of a [110] GaAs quantum well [Sih {\it et al.}, Nature Physics 1, 31 (2005)]. Working within the framework of the exact linear response formalism we calculate the spin-Hall conductivity including the Dresselhaus linear and cubic terms in the band structure, as well as the electron-impurity scattering and electron-electron interaction to all orders. We show that the spin-Hall conductivity naturally separates into two contributions, skew-scattering and side-jump, and we propose an experiment to distinguish between them.