Chiral anomaly in non-relativistic systems: Berry curvature and chiral kinetic theory

TL;DR

This paper develops a kinetic theory framework to analyze the chiral anomaly in non-relativistic systems with non-linear dispersions, extending understanding beyond the relativistic Dirac and Weyl fermions.

Contribution

It introduces a semi-classical kinetic approach using Wigner functions to study chiral anomalies in systems with non-linear dispersions, highlighting Berry monopoles' role.

Findings

Chiral anomaly is influenced by Berry monopoles in momentum space.

The framework shows the anomaly can be enhanced or suppressed by Berry curvature windings.

Results aid in understanding transport phenomena in non-relativistic Weyl systems.

Abstract

Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the non-linear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with non-linear dispersions by using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles in momentum space and could be enhanced or suppressed due to the windings around the Berry monopoles. Our results can help understand the chiral anomaly-induced transport phenomena in non-relativistic systems.