Hall diffusion anomaly and transverse Einstein relation

TL;DR

This paper reveals that in anomalous Hall materials, transverse currents are governed by two distinct responses linked by an unconventional Einstein relation, challenging the traditional single-coefficient understanding.

Contribution

It introduces a new transverse Einstein relation for anomalous Hall materials, showing the existence of two separate Hall responses and their impact on transverse diffusion and conductivity.

Findings

Identification of two distinct Hall responses in anomalous Hall materials.

Derivation of an unconventional transverse Einstein relation.

Examples where Hall diffusion dominates over Hall conductivity.

Abstract

It is commonly believed that the current response of an electron fluid to a mechanical force (such as an electric field) or to a ``statistical force" (e.g., a gradient of chemical potential) are governed by a single linear transport coefficient - the electric conductivity. We argue that this is not the case in anomalous Hall materials. In particular, we find that transverse (Hall) currents manifest two distinct Hall responses governed by an unconventional {\it transverse} Einstein relation that captures an anomalous relation between the Hall conductivity and the Hall diffusion constant. We give examples of when the Hall diffusion anomaly is prominent, resulting in situations where the transverse diffusion process overwhelms the Hall conductivity and vice versa.