# Quantum Kinetic Theory of the Chiral Anomaly

## TL;DR

This paper develops a comprehensive quantum kinetic theory for magnetotransport in weakly disordered crystals, capturing Berry phase effects and applying it to Weyl semimetals to analyze the chiral anomaly.

## Contribution

It introduces a quantum kinetic equation that fully incorporates Berry phase effects and provides a systematic way to analyze magnetotransport phenomena.

## Key findings

- Chiral anomaly persists only with very weak intervalley scattering.
- The theory captures Berry phase corrections to the density of states.
- Application to Weyl semimetals demonstrates the impact of scattering on magnetoconductivity.

## Abstract

We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wavepacket dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wavepacket dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. We show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.