Quantum melting of generalized Wigner crystals in moire semiconductors
In plain words
At fractional fillings such as one electron per three moire sites, electrons in WSe2/WS2 order into crystals because of their repulsion (generalized Wigner crystals), and how these crystals turn into metals as the repulsion is weakened is unknown.
Precise statement
In WSe2/WS2 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.
What would settle it
Local imaging of charge order versus gate distance and density, with compressibility measurements locating each transition and its hysteresis.