Generalized Wigner crystallization in moiré materials

Recent experiments on the twisted transition metal dichalcogenide (TMD) materials have observed insulating states at fractional occupancy of the moiré bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the general problem of Wigner crystallization in the presence of an underlying (moiré) 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 MoSe₂ (among the homobilayers) and MoSe₂/WSe₂ or MoS₂/WS₂ (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. These crystals realized on a moiré 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.