Pseudo anomalous Hall effect in semiconductors and semimetals: A classical perspective

TL;DR

This paper shows that classical mechanisms, specifically Lorentz force effects in multi-valley models, can produce non-linear Hall effects in semiconductors and semimetals, challenging the attribution of such effects solely to quantum phenomena.

Contribution

It introduces a classical explanation for non-linear Hall effects using multi-valley models, emphasizing the role of carrier mobility anisotropy and charge coexistence.

Findings

Classical Lorentz force can produce non-linear Hall effects.

Non-linear Hall response is significant near charge neutrality.

Classical effects can match experimental magnitudes in ZrTe$_5$.

Abstract

We demonstrate that the non-linear field dependence in the Hall effect, often indistinguishable from the anomalous Hall effect, can be realized entirely within the classical mechanism due to the Lorentz force by analyzing multi-valley models for semiconductors and semimetals. The non-linear component in the Hall resistivity $\rho_H^{\rm NL}$ originates from carrier mobility anisotropy or the coexistence of different charges. Since $\rho_H^{\rm NL}$ is inversely proportional to the carrier difference between electrons and holes $\Delta n$, it exceeds its zero-field value near charge neutrality. As a practical example, we show that the magnitude of the classical non-linear Hall response in ZrTe$_5$ is comparable to the experimental values, underscoring the importance of accounting for classical contributions before attributing non-linear Hall effects to quantum mechanisms.