Sliding motion of a two-dimensional Wigner crystal in a strong magnetic field

TL;DR

This paper investigates the nonlinear sliding behavior of a two-dimensional Wigner crystal under strong magnetic fields, analyzing conductivity, disorder effects, and experimental comparisons.

Contribution

It introduces a high-velocity perturbation theory to compute nonlinear conductivity and correlation functions for a Wigner crystal in a magnetic field with disorder.

Findings

Disorder causes mainly transverse distortions in the sliding state.

Hall resistivity remains at its classical value.

The nonlinear conductivity matches experimental I-V characteristics near filling factor 1/5.

Abstract

We study the sliding state of a two-dimensional Wigner crystal in a strong magnetic field and a random impurity potential. Using a high-velocity perturbation theory, we compute the nonlinear conductivity, various correlation functions, and the interference effects arising in combined AC + DC electric effects, including the Shapiro anomaly and the linear response to an AC field. Disorder is found to induce mainly transverse distortions in the sliding state of the lattice. The Hall resistivity retains its classical value. We find that, within the large velocity perturbation theory, free carriers which affect the longitudinal phonon modes of the Wigner crystal do not change the form of the nonlinear conductivity. We compare the present sliding Wigner crystal in a strong magnetic field to the conventional sliding charge-density wave systems. Our result for the nonlinear conductivity agrees well with the $I-V$ characteristics measured in some experiments at low temperatures or large depinning fields, for the insulating phases near filling factor $\nu$ = 1/5. We summarize the available experimental data, and point out the differences among them.