Dynamical properties of the pinned Wigner crystal

TL;DR

This paper investigates the dynamical behavior of a weakly pinned Wigner crystal in high magnetic fields, revealing how disorder and magnetic field influence its conductivity and pinning characteristics.

Contribution

It introduces a Gaussian variational approach to compute frequency and field-dependent conductivities of the pinned Wigner crystal, highlighting novel magnetic field effects.

Findings

Hall resistivity remains classical and frequency-independent at zero temperature.

Pinning peak and threshold electric field show distinct magnetic field dependences.

Conductivity spectra depend on the system's inherent length scales.

Abstract

We study various dynamical properties of the weakly pinned Wigner crystal in a high magnetic field. Using a Gaussian variational method we can compute the full frequency and field dependence of the real and imaginary parts of the diagonal and Hall conductivities. The zero temperature Hall resistivity is independent of frequency and remains unaffected by disorder at its classical value. We show that, depending on the inherent length scales of the system, the pinning peak and the threshold electric field exhibit strikingly different magnetic field dependences.