Side jump contribution to spin-orbit mediated Hall effects and Berry curvature

TL;DR

This paper explores how spin-orbit coupling influences Hall effects and Berry curvature in semiconductors, highlighting the role of anomalous operators and their symmetry properties.

Contribution

It provides a detailed analysis of the relation between anomalous coordinate and velocity operators and Berry curvature in GaAs-type semiconductors, including symmetry considerations.

Findings

Berry curvature relates to anomalous operators in the ${f k} imes{f p}$ formalism.

Transformational properties of Berry curvature are characterized for centrosymmetric semiconductors.

The study clarifies the connection between spin-orbit effects and Hall phenomena in semiconductors.

Abstract

Anomalous Hall effect and spin Hall effect originate due to spin-orbit coupling that in the Kohn-Luttinger ${\bf k}\cdot{\bf p}$ formalism is represented by anomalous terms in the coordinate and velocity operators. Relation of these operators to the Berry curvature in the momentum space is presented for electrons in GaAs type semiconductors. For centrosymmetric semiconductors, transformational properties of Berry curvature are discussed.