Nonlinear Wigner solid transport over superfluid helium under AC conditions

TL;DR

This study investigates the nonlinear transport behavior of a two-dimensional Wigner solid of surface electrons on superfluid helium under AC conditions, revealing frequency-dependent phenomena and new oscillatory regimes in the presence of ripplon interactions.

Contribution

It provides a general solution for the field-velocity relationship under AC conditions, highlighting the impact of current frequency on Bragg-Cherenkov resonances and ripplon interactions, which was not previously understood.

Findings

Field-velocity characteristics differ from DC theory.

Low-frequency currents produce saw-tooth Bragg-Cherenkov resonances.

High-frequency currents lead to oscillatory Bragg-Cherenkov regimes.

Abstract

Nonlinear transport properties of the two-dimensional Wigner solid of surface electrons on superfluid helium are studied for alternating current conditions. For time-averaged quantities like Fourier coefficients, the field-velocity characteristics are shown to be qualitatively different as compared to that found in the DC theory. For a spatially uniform current we found a general solution for the field-velocity relationship which appears to be strongly dependent on the current frequency. If the current frequency is much lower than the ripplon damping parameter, the Bragg-Cherenkov resonances which appear at high enough drift velocities acquire a distinctive saw-tooth shape with long right-side tails independent of small damping. For current frequencies which are close or higher than the ripplon damping coefficient, the interference of ripplons excited at different time intervals results in a new oscillatory (in drift velocity) regime of Bragg-Cherenkov scattering.