Melting of the two-dimensional wigner crystal in the quantum region

Valerii T. Dolgopolov

Erdal Eren Uğurcuklu

Dyuti Bhattacharya, Alexei V. Filinov, Amit Ghosal +1 more

DinhDuy Vu, S. Das Sarma

We consider the 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.

Houman Falakshahi, Xavier Waintal

We study the quantum melting of the two-dimensional Wigner crystal using a fixed node quantum Monte Carlo approach. In addition to the two already known phases (Fermi liquid at large density and Wigner crystal at low density), we find a third stable phase at intermediate values of the density. The third phase has hybrid behaviors in between a liquid and a solid. This hybrid phase has the nodal structure of a Slater determinant constructed out of the bands of a triangular lattice.