Anomalous Hall effect in a two-dimensional electron gas

TL;DR

This paper investigates the anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling, revealing how disorder and subband occupation influence the Hall conductivity.

Contribution

It provides a detailed theoretical analysis of the anomalous Hall effect considering disorder effects and clarifies discrepancies in previous studies.

Findings

All contributions vanish when both chiral subbands are occupied.

Skew scattering dominates when only the majority subband is occupied.

Results reconcile previous conflicting theoretical treatments.

Abstract

The anomalous Hall effect in a magnetic two-dimensional electron gas with Rashba spin-orbit coupling is studied within the Kubo-Streda formalism in the presence of pointlike potential impurities. We find that all contributions to the anomalous Hall conductivity vanish to leading order in disorder strength when both chiral subbands are occupied. In the situation that only the majority subband is occupied, all terms are finite in the weak scattering limit and the total anomalous Hall conductivity is dominated by skew scattering. We compare our results to previous treatments and resolve some of the discrepancies present in the literature.