Relation Between the Spin Hall Conductivity and the Spin Chern Number for Dirac-like Systems

TL;DR

This paper introduces a semiclassical approach to the spin Hall effect in Dirac-like systems, showing that the spin Chern number predominantly determines the spin Hall conductivity, regardless of spin conservation.

Contribution

It establishes a connection between the spin Hall conductivity and the spin Chern number in Dirac-like systems, including cases with spin non-conservation.

Findings

Spin Chern number dominates spin Hall conductivity

Application to Kane-Mele model of graphene

Effect of Rashba spin-orbit coupling analyzed

Abstract

A semiclassical formulation of the spin Hall effect for physical systems satisfying Dirac-like equation is introduced. We demonstrated that the main contribution to the spin Hall conductivity is given by the spin Chern number whether the spin is conserved or not at the quantum level. We illustrated the formulation within the Kane-Mele model of graphene in the absence and in the presence of the Rashba spin-orbit coupling term.