Cyclotron-Bloch dynamics of a quantum particle in a 2D lattice

TL;DR

This paper investigates the quantum behavior of a charged particle in a 2D lattice under electric and magnetic fields, revealing conditions for directed transport and ballistic spreading, and analyzing the impact of disorder.

Contribution

It introduces a detailed analysis of quantum transport in a 2D lattice with electric and magnetic fields, including the effects of initial conditions and disorder.

Findings

Directed drift occurs only for specific initial conditions and low electric field magnitudes.

Ballistic spreading of the wave packet occurs outside the drift regime.

Disorder influences the quantum dynamics and transport properties.

Abstract

This paper studies the quantum dynamics of a charged particle in a 2D square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave--packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions insuring directed transport with the drift velocity. We also describe the effect of disorder in the system.