Landauer-B\"uttiker Study of the Anomalous Hall Effect

TL;DR

This study uses Landauer-Büttiker formalism to analyze anomalous Hall effect in a 2D electron gas with Rashba spin-orbit coupling and magnetization, revealing the relationship between density of states and Hall conductance.

Contribution

It provides a numerical investigation of the anomalous Hall effect in disordered and ballistic 2D systems, connecting conductance peaks to density of states singularities and analyzing magnetization effects.

Findings

Hall conductance peaks near the lower band edge.

Suppression of Hall conductance at large magnetization.

Close connection between density of states and Hall conductance.

Abstract

We report on Landauer-B\"uttiker studies of anomalous Hall transport in a two-dimensional electron gas with Rashba spin-orbit coupling and a magnetization provided by localized magnetic moments. Our system is described by a discretized tight-binding model in a four-terminal geometry. We consider both the case of magnetically disordered systems as well as ballistic transport in disorder-free systems with spatially homoge- neous magnetization. In the latter case we investigate both out-of-plane and in-plane magnetizations. We numerically establish a close connection between singularities in the density of states and peaks in the Hall conductance close to the lower band edge. Consistent with previous theoretical studies based on diagrammatic perturbation expansions, these peaks occur at Fermi energies where only the lower dispersion branch is occupied. Moreover, for large magnetization the Hall conductance is, along with the density of states, sup- pressed. This numerical finding can be understood from analytical properties of the underlying model in the limit of an infinite system.