Berry’s phase and the anomalous velocity of Bloch wavepackets

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 Berry’s phase acquired by adjacent Bloch states within a wavepacket.

Figure 1

$k$-space line integrals giving rise to the Berry’s phases in Eq. (16).