Melting temperature shifts from quantum fluctuations in generalized Wigner crystals

Abstract

It is generally believed that quantum fluctuations collaborate with thermal fluctuations, effectively reducing transition temperatures (e.g. for melting of charge order). We show that this is not always the case and that the interplay between quantum and thermal fluctuations can be competitive. We find excellent motivation for addressing this thanks to the discovery of correlated insulating "generalized Wigner crystal" (GWC) states in hetero-bilayer transition metal dichalcogenide (WS$_2$/WSe$_2$) moir\'e systems [Y. Xu, et al., Nature 587, 214-218 (2020)]. We account for the impact of quantum effects on the melting temperature of GWCs, carrying out finite temperature Lanczos calculations on an extended Hubbard model on the triangular lattice (both with a double-gate screened potential, and the nearest neighbor model) for multiple electron densities. We show that quantum effects capture the shift relative to the classical estimates, which in some cases are more than 50 percent off from the experimental values. Then building on these numerical findings, we provide a qualitative picture that clarifies that while quantum melting of GWC (by increasing the bandwidth) naturally softens the ground state order parameter, it does not always decrease the melting temperature; conversely it can increase it. To do so we employ a finite temperature perturbation theory, treating the kinetic energy perturbatively on top of a classical Wigner crystal. Our predictions should be observable in future experiments where the bandwidth can be tuned.