Bloch dynamics with second order Berry phase correction

TL;DR

This paper derives an advanced semiclassical Bloch dynamics framework incorporating second-order Berry phase corrections using two-scale WKB analysis, confirming gauge independence and aligning with recent findings.

Contribution

It introduces a second-order Berry phase correction into Bloch dynamics derivation, extending previous models with a rigorous mathematical approach.

Findings

Bi-characteristics system matches previous results under uniform electric field.

Extra terms in bi-characteristics are gauge independent with linear electric fields.

The derivation confirms consistency with recent theoretical developments.

Abstract

We derive the semiclassical Bloch dynamics with the second-order Berry phase correction in the presence of the slow-varying scalar potential as perturbation. Our mathematical derivation is based on a two-scale WKB asymptotic analysis. For a uniform external electric field, the bi-characteristics system after a positional shift introduced by Berry connections agrees with the recent result in previous works. Moreover, for the case with a linear external electric field, we show that the extra terms arising in the bi-characteristics system after the positional shift are also gauge independent.