Berry Electrodynamics - Anomalous Drift and Pump from Electric Field Analog

Berry curvature can significantly affect the dynamics of a wave packet in a 2D Bloch band. It gives rise to a Hall drift and thus can be treated as an analog of magnetic field in quasi-momentum space. Indeed, we can even define an Electric field analog from the time derivative of the Berry connection. This analog field appears as an anomalous velocity and integrates into a transverse drift in the semi-classical equation of motion for a wave packet undergoing adiabatic evolution in a Bloch band. Time-dependent Berry connection can lead to interesting results in non-adiabatic processes as well. An anomalous drift proportional to a shift vector is observed during band switching. This shift vector depends not only on the topological properties of the involved bands but also on the nature of drive. In some special cases, band population can be flipped without a significant anomalous drift. We simulate these effects and show that a combination of adiabatic and non-adiabatic steps in a cycle can amplify the transverse drift due to the Electric field analog, and can be combined to provide a persistent pumping effect.