Dynamical localization for Bloch electrons in Magnetic and Electric Fields

TL;DR

This paper investigates how magnetic and electric fields influence electron wave packet dynamics in a 2D periodic system, revealing electric field-induced localization effects and the impact of field orientation on electron localization.

Contribution

It provides a comprehensive analysis of wave packet evolution considering Landau level coupling and field effects, highlighting localization phenomena due to electric fields and lattice orientation.

Findings

Electric field causes localization along its direction.

Incommensurate field orientation leads to localization in both directions.

Energy levels are quantized with respect to longitudinal quasi-momentum.

Abstract

We study the time evolution of wave packets of noninteracting electrons in a two-dimensional periodic system in the presence of magnetic and electric fields. The model includes consistently the coupling between Landau levels as well as the periodic and external field contributions. It is shown that the electric field produces localization along its longitudinal direction, this effect is a physical consequence of the quantization of the energy levels with respect to the longitudinal quasi-momentum. For incommensurate orientations of $\mathbf{E}$ relative to the lattice the wave packet becomes localized in both directions.