Extrinsic anomalous Hall conductivity of a topologically nontrivial conduction band

TL;DR

This paper investigates the extrinsic anomalous Hall effect in topologically nontrivial conduction bands, focusing on impurity scattering contributions like side-jump and skew-scattering, and their dependence on carrier density.

Contribution

It provides a detailed calculation of extrinsic Hall conductivities considering both nonmagnetic and magnetic impurities in a quantum anomalous Hall system.

Findings

Side-jump Hall conductivity changes sign at a critical carrier density.

Critical densities are within experimentally accessible ranges.

Results suggest identifying quantum anomalous Hall systems in the good-metal regime.

Abstract

A key step towards dissipationless transport devices is the quantum anomalous Hall effect, which is characterized by an integer quantized Hall conductance in a ferromagnetic insulator with strong spin-orbit coupling. In this work, the anomalous Hall effect due to the impurity scattering, namely the extrinsic anomalous Hall effect, is studied when the Fermi energy crosses with the topologically nontrivial conduction band of a quantum anomalous Hall system. Two major extrinsic contributions, the side-jump and skew-scattering Hall conductivities, are calculated using the diagrammatic techniques in which both nonmagnetic and magnetic scattering are taken into account simultaneously. The side-jump Hall conductivity changes its sign at a critical sheet carrier density for the nontrivial phase, while it remains sign unchanged for the trivial phase. The critical sheet carrier densities estimated with realistic parameters lie in an experimentally accessible range. The results imply that a quantum anomalous Hall system could be identified in the good-metal regime.