Thermal melting of a quantum electron solid in the presence of strong disorder: Anderson versus Wigner

TL;DR

This paper investigates how strong disorder influences the temperature-driven melting of Wigner solids in 1D and 2D electron systems, revealing that disorder can significantly increase the melting temperature due to localization effects.

Contribution

It demonstrates that disorder can enhance the melting temperature of Wigner crystals by inducing a localized glassy state, combining Anderson localization and Wigner crystallization physics.

Findings

Disorder can strongly increase the effective melting temperature.

Localized glassy states form due to combined Anderson and Wigner physics.

Experimental observations of insulating Wigner solids can occur above the pristine melting temperature.

Abstract

We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.