Theory of generalized Wigner crystals in moire superlattices.

Recent developments in moire materials (twisted layers of graphene or transition metal compounds) has opened up a new avenue to realize quasi-flat bands in condensed matter systems in which the interactions dominate. Our previous calculations suggested that the correlations in such systems could be strong enough to realize electronic solids called Wigner crystals (WC). Such states have been observed before in (continuum) 2D electron gas and recently it was also claimed to be observed in a (moire lattice of) twisted bilayer of WS/WSe2. Despite the experimental advances, a clear understanding of the physics of WC coupled to an underlying lattice is completely lacking. In this talk we present some preliminary results based on a model we construct to address this problem. In such a scenario, melting of a WC (coupled to lattice) can be understood in terms of an interplay of coulomb interaction and the tendency for forming solitons.