Semiclassical Boltzmann magnetotransport theory in anisotropic systems with a nonvanishing Berry curvature

TL;DR

This paper develops a semiclassical Boltzmann transport theory for anisotropic topological materials with Berry curvature, revealing how magnetic fields induce anisotropic relaxation times and affect conductivity.

Contribution

It introduces a comprehensive framework incorporating anisotropy and Berry curvature effects into magnetotransport calculations in topological systems.

Findings

Magnetic field and Berry curvature coupling leads to anisotropic relaxation times.

Calculated conductivity shows significant deviation from constant relaxation time models.

Effective mean-free-path vector is derived from an integral equation considering anisotropy.

Abstract

Understanding the transport behavior of an electronic system under the influence of a magnetic field remains a key subject in condensed matter physics. Particularly in topological materials, their nonvanishing Berry curvature can lead to many interesting phenomena in magnetotransport owing to the coupling between the magnetic field and Berry curvature. By fully incorporating both the field-driven anisotropy and inherent anisotropy in the band dispersion, we study the semiclassical Boltzmann magnetotransport theory in topological materials with a nonvanishing Berry curvature. We show that as a solution to the Boltzmann transport equation the effective mean-free-path vector is given by the integral equation, including the effective velocity arising from the coupling between the magnetic field, Berry curvature and mobility. We also calculate the conductivity of Weyl semimetals with an isotropic energy dispersion, and find that the coupling between the magnetic field and Berry curvature induces anisotropy in the relaxation time, showing a substantial deviation from the result obtained assuming a constant relaxation time.