Visualizing the impact of quenched disorder on 2D electron Wigner solids

Electron Wigner solids (WSs)^1-12 provide an ideal system for understanding the competing effects of electron-electron and electron-disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has been limited by a lack of single-defect-resolved experimental measurements as well as accurate theoretical tools to enable realistic experiment/theory comparison. Here we overcome these limitations by combining atomically resolved scanning tunnelling microscopy (STM) with neural-quantum-state quantum Monte Carlo (NQS-QMC) simulation of disordered 2D electron WSs to discover new disorder-induced physical regimes of correlated electron behaviour. STM was used to image the electron density (n_e)-dependent evolution of electron WSs in gate-tunable bilayer MoSe₂ (BL-MoSe₂) devices with varying long-range (n_LR) and short-range (n_SR) disorder densities. These images were compared with NQS-QMC simulations using realistic disorder maps extracted from experiment, thus allowing the roles of different disorder types to be disentangled. We identify two distinct physical regimes for disordered electron WSs that depend on n_SR. For n_SR ≲ n_e, the WS behaviour is dominated by long-range disorder and features extensive mixed solid-liquid phases, a new type of local re-entrant melting/crystallization and prominent Friedel oscillations. By contrast, when n_SR ≫ n_e, these features are suppressed and a more robust amorphous WS phase emerges that persists to higher n_e, highlighting the importance of short-range disorder in this regime. Our work establishes a powerful framework for studying disordered quantum solids through a combined experimental-theoretical approach.