Melting, Reentrant Ordering and Peak Effect for Wigner Crystals with Quenched and Thermal Disorder

TL;DR

This paper uses simulations to explore how thermal fluctuations and quenched disorder influence Wigner crystal phases, revealing reentrant ordering and peak effect phenomena similar to superconducting vortices.

Contribution

It demonstrates the interplay of thermal and quenched disorder in Wigner crystals, showing reentrant order and peak effects through transport response analysis.

Findings

Reentrant ordered phase due to thermal fluctuations reducing quenched disorder effects

Increase in mobility or depinning transition indicating reentrant ordering

Peak effect-like drop in electron mobility during thermal melting

Abstract

We consider simulations of Wigner crystals interacting with random quenched disorder in the presence of thermal fluctuations. When quenched disorder is absent, there is a well defined melting temperature determined by the proliferation of topological defects, while for zero temperature, there is a critical quenched disorder strength above which topological defects proliferate. When both thermal and quenched disorder are present, these effects compete, and the thermal fluctuations can reduce the effectiveness of the quenched disorder, leading to a reentrant ordered phase in agreement with the predictions of Nelson [Phys. Rev. B 27, 2902 (1983)]. The onset of the reentrant phase can be deduced based on changes in the transport response, where the reentrant ordering appears as an increase in the mobility or the occurrence of a depinning transition. We also find that when the system is in the ordered state and thermally melts, there is an increase in the effective damping or pinning. This produces a drop in the electron mobility that is similar to the peak effect phenomenon found in superconducting vortices, where thermal effects soften the lattice or break down its elasticity, allowing the particles to better adjust their positions to take full advantage of the quenched disorder.