Berry-electrodynamics - Anomalous drift and pumping from time-dependent Berry connection

TL;DR

This paper investigates how time-dependent Berry connection induces anomalous drift and pumping in wave packet motion within Bloch bands, revealing new effects from periodic driving and cyclic evolution in reciprocal space.

Contribution

It introduces the concept of an electric field analog in reciprocal space from time-dependent Berry connection and demonstrates its role in anomalous drift and pumping phenomena.

Findings

Time-dependent Berry connection causes anomalous drift in wave packets.

Periodic driving leads to drift dependent on the drive's nature.

Cyclic evolution in momentum space results in net anomalous pumping.

Abstract

The Berry curvature of a Bloch band can be interpreted as a local magnetic field in reciprocal space. This analogy can be extended by defining an electric field analog in reciprocal space which arises from the time-dependent Berry connection. We explore the term in the semi-classical equation of motion that gives rise to this phenomenon, and show that it can lead to anomalous drift in wave packet motion. A similar effect arises from changes in the band population due to periodic driving, where the resulting drift depends on the nature of the drive and can be expressed in terms of a shift vector. Finally, these effects can be combined to build a pump with a net anomalous drift during a cyclic evolution in momentum space.