Affiliations: [a] Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham NC 27708, USA. E-mail: jianfeng@math.duke.edu | [b] School of Mathematical Sciences, Peking University, Beijing, 100871, China. E-mail: zhang-zihang@pku.edu.cn | [c] Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China. E-mail: zhennan@bicmr.pku.edu.cn
Abstract: We derive the semiclassical Bloch dynamics with 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.
