Dynamics of the effective mass and the anomalous velocity in two-dimensional lattices

TL;DR

This paper investigates how sudden application of a force affects the effective mass and anomalous velocity of wave packets in 2D lattices, providing analytical approximations and numerical validation.

Contribution

It introduces semianalytical expressions for dynamical corrections to velocities in 2D lattices with Berry curvature, extending the semiclassical model for sudden forces.

Findings

Excellent agreement between analytical and numerical results for weak forces.

Dynamical corrections significantly influence velocities in certain regimes.

Potential for experimental detection of these effects.

Abstract

The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time and space, so that the particle described by the wave packet has time to respond according to the properties of the lattice. We analyze the dynamical corrections to this picture when a uniform force is suddenly applied, identifying separate corrections to the usual group and anomalous velocities. We find approximate semianalytical expressions for generalized "dynamical" group and anomalous velocities, and the associated accelerations. We use a two-dimensional optical lattice with finite Berry curvature to illustrate the semianalytical approximation in a regime where the dynamical corrections are significant, suggesting the possibility of experiments to detect them; we compare the results with a full numerical solution, showing excellent agreement for weak forces.