Anomalous Hall response of topological insulators

TL;DR

This paper analyzes the anomalous Hall effect in 3D topological insulators, showing that the intrinsic topological term dominates over other contributions, providing a clear signature of $Z_2$ topological order.

Contribution

It systematically evaluates various contributions to the anomalous Hall effect, revealing the dominance of the topological term and identifying a new intrinsic side-jump component.

Findings

Topological term dominates the Hall response even with disorder

Skew scattering contributes beyond the Born approximation

A novel intrinsic side-jump term is identified

Abstract

The anomalous Hall effect due to the surface conduction band of 3D topological insulators with an out-of-plane magnetization is \textit{always} dominated by an intrinsic topological term of the order of the conductivity quantum. We determine the contributions due to the band structure, skew scattering, side jump and magnetic impurities on the same footing, demonstrating that the topological term, renormalized due to disorder, overwhelms all other terms, providing an unmistakable signature of $Z_2$ topological order. Uncharacteristically, skew scattering contributes in the Born approximation as well as in the third order in the scattering potential, while in addition to the side-jump scattering term we identify a novel intrinsic side-jump term of a similar magnitude. These, however, never overwhelm the topological contribution.