Generalized Wigner crystallization in moir\'e materials

TL;DR

This paper investigates the formation of generalized Wigner crystals in moiré TMD materials, identifying optimal candidates and analyzing their properties, including the effects of lattice pinning and low-energy excitations.

Contribution

It provides a theoretical analysis of Wigner crystallization in moiré TMDs, identifying specific materials as promising candidates and modeling their low-energy excitations with a Sine-Gordon theory.

Findings

MoSe₂ and MoSe₂/WSe₂ are ideal for realizing GWCs.

Hole-crystals are easier to realize than electron-crystals due to larger effective mass.

GWC formation occurs at densities far below the Mott insulating regime.

Abstract

Recent experiments on the twisted transition metal dichalcogenide (TMD) material, $\rm WSe_2/WS_2$, have observed insulating states at fractional occupancy of the moir\'e bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the problem of Wigner crystallization in the presence of an underlying (moir\'e) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_{s}$ indicates that $\rm MoSe_{2}$ (among the homobilayers) and $\rm MoSe_2/WSe_2$ or $\rm MoS_2/ WS_2$ (among the heterobilayers) are the best candidates for realizing GWCs. We also establish that due to larger effective mass of the valence bands, in general, hole-crystals are easier to realize that electron-crystals as seen experimentally. For completeness, we show that satisfying the Mott criterion $n_{\rm Mott}^{1/2} a_{\ast} = 1$ requires densities nearly three orders of magnitude larger than the maximal density for GWC formation. This indicates that for the typical density of operation, HoM or HeM systems are far from the Mott insulating regime. These crystals realized on a moir\'e lattice, unlike the conventional Wigner crystals, are incompressible due the gap arising from pinning with the lattice. Finally, we capture this many-body gap by variationally renormalizing the dispersion of the vibration modes. We show these low-energy modes, arising from coupling of the WC with the moir\'e lattice, can be effectively modeled as a Sine-Gordon theory of fluctuations.