Gauge Potential Formulations of the Spin Hall Effect in Graphene

TL;DR

This paper explores gauge potential approaches to calculate the spin Hall conductivity in graphene, employing Berry gauge fields and Foldy-Wouthuysen transformations to provide explicit formulations.

Contribution

It introduces two gauge potential methods for explicitly calculating spin Hall conductivity in graphene with spin-orbit interaction.

Findings

Both gauge fields can be derived from pure gauge fields via Foldy-Wouthuysen transformations.

The spin Hall conductivity can be formulated by requiring the vanishing of the time evolution of kinematic momentum.

Explicit expressions for spin Hall conductivity are obtained using Berry gauge fields.

Abstract

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.