Quantum melting of generalized Wigner crystals in moire semiconductors

In $\mathrm{WSe_2}$/$\mathrm{WS_2}$ and similar heterobilayers, insulating states at fractional fillings $\nu = 1/3, 1/2, 2/3$ and others were detected optically (Regan et al., Nature, 2020, arXiv:1910.09047) and later imaged. As the ratio of Coulomb energy to bandwidth, or the screening length set by gate distance, is reduced, determine whether each crystal melts into a Fermi liquid directly (first or second order) or through intermediate phases such as stripes, bubbles, microemulsions or a quantum-melted state without charge order but with insulating transport. An answer is a phase diagram versus $\nu$ and screening length with the order of each transition.

Local imaging of charge order versus gate distance and density, with compressibility measurements locating each transition and its hysteresis.