Anomalous Hall conductivity and quantum friction

TL;DR

This paper investigates the anomalous Hall effect in clean 2D systems using a network model, revealing boundary-sensitive contributions and drawing analogies to viscous fluid friction.

Contribution

It introduces a two-part model of Hall conductivity, distinguishing bulk and boundary effects, offering a new interpretation of phenomena in high-conductivity regimes.

Findings

Boundary-sensitive component scales with system width

Bulk component aligns with Kubo formula predictions

Provides an alternative explanation to skew scattering in clean samples

Abstract

Anomalous Hall effect in very clean samples (high conductivity regime) is studied using a two-dimensional network model. We find that the off-diagonal conductivity comprises two parts: one which reflects the bulk properties as obtained by the Kubo formula and another which is sensitive to boundary conditions imposed on the network. The latter scales with the system width in the ideal case and for real-world samples, it will depend on the coherence length. It provides an alternative interpretation of the observed behaviour in the clean limit which is otherwise attributed to the skew scattering. We highlight analogies to friction in viscous fluids responsible for Couette flow.