Melting, reentrant ordering and peak effect for Wigner crystals with quenched and thermal disorder

Abstract

We consider simulations of Wigner crystals in solid state systems 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)]. There are two competing theories for the low temperature behavior, and our simulations show that both capture aspects of the actual response. The critical disorder strength separating ordered from disordered states remains finite as the temperature goes to zero, as predicted by Cha and Fertig [Phys. Rev. Lett. 74, 4867 (1995)], instead of dropping to zero as predicted by Nelson. At the same time, the critical disorder strength decreases with decreasing temperature, as predicted by Nelson, instead of remaining constant, as predicted by Cha and Fertig. 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.

Noise and thermal depinning of Wigner crystals

“…For T/T m = 1.03, the system is disordered for all values of F p and the velocity is even higher but has a gradual drop with increasing F p , and the same trend occurs for T/T m = 1.36. A more detailed study of the general phase diagram for the disordered and ordered phases as a function of pinning strength versus temperature appears in [76]. The results in figures 1 and 2 indicate that the system exhibits three distinct regimes.…”

“…Throughout this work we fix n = 0.208 and n p = 0.25. At T = 0 and in the absence of quenched disorder, the charges form a triangular lattice that has a well defined melting transition temperature T m [76]. Additionally, when T = 0 there is a well defined quenched disorder strength above which the system disorders [76].…”

“…At T = 0 and in the absence of quenched disorder, the charges form a triangular lattice that has a well defined melting transition temperature T m [76]. Additionally, when T = 0 there is a well defined quenched disorder strength above which the system disorders [76]. We represent the charges using a previously studied model [52,65,[75][76][77][78][79][80], where the equation of motion for charge i is…”

“…Additionally, when T = 0 there is a well defined quenched disorder strength above which the system disorders [76]. We represent the charges using a previously studied model [52,65,[75][76][77][78][79][80], where the equation of motion for charge i is…”

“…We consider samples with F p = 0.5, a pinning strength at which the charges are disordered for T/T m = 0, so the system is in a strongly disordered glass phase. The T/T m = 0 plastic depinning that occurs in this regime was studied in detail in [76], where a pinned phase, a filamentary flow phase, a disordered flow phase, and a dynamically ordered moving smectic phase (MS) appear in sequence as a function of increasing drive.…”