Berry's phase and the anomalous velocity of Bloch wavepackets

TL;DR

This paper explains the anomalous velocity of Bloch electrons in semiclassical dynamics as a consequence of Berry's phase differences acquired by neighboring states, linking geometric phases to electron motion.

Contribution

It provides a novel interpretation of the anomalous velocity in terms of Berry's phase differences within a wavepacket, enhancing understanding of semiclassical electron dynamics.

Findings

Anomalous velocity arises from Berry's phase differences.

Adiabatic evolution in a changing vector potential explains the effect.

Berry connection acts as a vector potential in k-space.

Abstract

The semiclassical equations of motion for a Bloch electron include an anomalous velocity term analogous to a $k$-space "Lorentz force", with the Berry connection playing the role of a vector potential. By examining the adiabatic evolution of Bloch states in a monotonically-increasing vector potential, I show that the anomalous velocity can be explained as the difference in the Berry's phase acquired by adjacent Bloch states within a wavepacket.