Drive Dependence of the Hall Angle for a Sliding Wigner Crystal in a Magnetic Field

TL;DR

This study numerically investigates how quenched disorder influences the Hall angle in a driven Wigner crystal under a magnetic field, revealing a drive-dependent behavior due to a side jump effect.

Contribution

It demonstrates that disorder induces a drive-dependent Hall angle in a Wigner crystal, a phenomenon not observed in the disorder-free case, highlighting a generic feature of classical charges with quenched disorder.

Findings

Hall angle is near zero at depinning and increases linearly with drive

The Hall angle saturates close to the disorder-free value at high drives

Drive dependence is due to a side jump effect during charge motion over pinning sites

Abstract

We numerically examine the depinning and sliding dynamics of a Wigner crystal in the presence of quenched disorder and a magnetic field. In the disorder-free limit, the Wigner crystal Hall angle is independent of crystal velocity, but when disorder is present, we find that Hall angle starts near zero at the depinning threshold and increases linearly with increasing drive before reaching a saturation close to the disorder free value at the highest drives. The drive dependence is the result of a side jump effect produced when the charges move over pinning sites. The magnitude of the side jump is reduced at the higher velocities. The drive dependent Hall angle is robust for a wide range of disorder parameters and should be a generic feature of classical charges driven in the presence of quenched disorder and a magnetic field.