Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

TL;DR

This paper develops a unified semiclassical wave-packet theory for electrons in slowly perturbed crystals, incorporating gradient corrections and Berry-phase effects, applicable to electromagnetic and lattice deformations.

Contribution

It derives a comprehensive wave-packet energy and Berry-phase terms for various perturbations, including electromagnetic fields and crystal deformations, without inter-band couplings.

Findings

Recovered orbital magnetization energy and anomalous velocity within a single-band framework.

Identified Berry-phase contributions due to lattice tracking and dislocations.

Established proportionality of Berry phase to Burgers vector around dislocations.

Abstract

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.