Modelling the Density-Tuned Wigner Solid Transition in Disordered TMD homobilayers

A recent experiment by Zhang et al. (2510.12009) employs atomically resolved scanning tunneling microscopy (STM) to image the electron density in gate-tunable bilayer MoSe₂ and to resolve both long-range (charged) and short-range (neutral) disorder in the system. The experiment reports that, in the presence of disorder, the Wigner solid phase in this material persists to much lower values of the Wigner–Seitz radius (r_S) than predicted by Quantum Monte Carlo simulations of clean systems.

In this work, we analyse the experimental data within the framework of Anderson localisation. Approaching from the metallic side, we compute the zero-temperature relaxation time arising from scattering of the charged carriers due to uncharged (short-range) and charged (long-range) impurities, accounting for screening by the charged carriers themselves in the latter case. We use this to assess the effect of Anderson localisation, employing the Ioffe–Regel–Mott criterion, on the persistent Wigner solid behaviour.