Is disorder both friend and foe to melting of Wigner-Mott insulators? – Part 1

Wigner crystals are extremely fragile due to strong geometric frustration inherent in long-range Coulomb interactions. This fragility is physically manifested in a very small characteristic energy scale associated with shear (density) fluctuations, which are gapless excitations in a translationally invariant system. However, the presence of disorder breaks translational invariance, suppressing these gapless excitations and pushing the system toward higher density before melting occurs. In the first part of the talk, motivated by recent experiments, we illustrate this general principle motivating a microscopic model. We describe the melting process via a generalized Lindemann criterion, which states that melting occurs when the ``bond” fluctuations—whether thermal or quantum—become comparable to the lattice spacing. To better understand the observed phase coexistence in such systems, we define a local marker that captures the spatial features associated with solid-liquid coexistence.