Absence of Hall effect due to Berry curvature in phase space

Takehito Yokoyama

doi:10.1038/s41598-021-91436-4

Abstract

Transverse current due to Berry curvature in phase space is formulated based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet. It is shown that the Hall effect due to the phase space Berry curvature is absent because the contributions from “anomalous velocity” and “effective Lorentz force” are completely cancelled out.

Highlights

We investigate transverse current due to Berry curvature in phase space based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet
It is shown that the Hall effect due to the Berry curvature in phase space is absent because the contributions from “anomalous velocity” and “effective Lorentz force” are completely cancelled out
We will show that Hall effect due to phase space Berry curvature is absent

Summary

Introduction

Transverse current due to Berry curvature in phase space is formulated based on the Boltzmann equations with the semiclassical equations of motion for an electron wave packet. Berry curvature in momentum space has a correction to the group velocity of the band dispersion which is perpendicular to the group velocity, anomalous velocity, leading to anomalous Hall effect[10,11]. Berry curvature in real space has a correction to the external electric field (force) which is perpendicular to the electric field, resulting in topological Hall effect[12,13].

Results

Conclusion