Relation between the spin Hall conductivity and the spin Chern number for Dirac-like systems


Dayı Ö. F. , YUNT E.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.13, no.1, 2016 (SCI-Expanded) identifier identifier

Abstract

A semiclassical formulation of the spin Hall effect for physical systems satisfying Dirac-like equation is introduced. We demonstrate 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.