Current density in the anomalous Hall effect regime under weak scattering

TL;DR

This paper investigates the equilibrium and differential current density patterns in the anomalous Hall effect regime, revealing robustness differences between edge and middle channels and their impact on conductance.

Contribution

It provides a detailed analysis of current density patterns in AHE systems, highlighting the robustness of edge channels and the width-independence of Hall conductance under certain conditions.

Findings

Edge channels are more robust against scattering than middle channels.

Differential current density forms a snaking pattern across the ribbon.

Hall conductance remains independent of ribbon width within specific scattering regimes.

Abstract

A finite equilibrium current density arises in the anomalous Hall effect (AHE) as a result of time-reversal symmetry breaking, affecting both the differential current density and total current. This study illustrates the equilibrium current density pattern in a ribbon-shaped system within the AHE regime, consisting of two sets of counterpropagating channels arranged in a zebra crossing pattern. While the middle channels are susceptible to scattering, the edge channels remain relatively robust. Despite this difference, all channels exhibit the same differential current density when subjected to a differential voltage across the two ends of the ribbon. When a differential voltage is applied to both sides of the ribbon, it results in a snaking pattern of differential current density forming across it. Furthermore, in a four-terminal device comprising an AHE ribbon and two normal leads, it is found that Hall conductance is independent of ribbon width within certain scattering strengths due to differences in robustness between middle and edge channels. These findings underscore the significant role played by current density in AHE transport.