Visualizing Frenkel–Kontorova Crystals Under Competing Coulomb and Moiré Potentials

Frenkel–Kontorova (FK) Model captures the behavior of interacting particles within a periodic substrate potential, often in a one-dimensional chain with only nearest-neighbor interaction considered. It provides a fundamental framework to understand how competing interactions and periodicity give rise to rich phenomena such as commensurability, solitons, and friction at the atomic scale.Here we demonstrate that moiré superlattices in van der Waals heterostructures with weak potentials form a highly controllable platform for realizing two-dimensional FK model. We directly image the evolution of a hole Wigner crystal modulated by a weak moiré potential, under different interaction regimes tuned by carrier density using scanning tunneling microscopy. With varying doping, the phase of the Wigner crystal is pinned by moiré wavevectors of comparable values, leading to determined rotations between low- and high-density configurations. By tuning density, we observe an Aubry transition: at enough high densities (n>n_c) with dominant Coulomb interactions, the hole crystal locked by the largest moiré wavevector enters a quasi-1D sliding mode with inter-chain interactions; slightly below the critical density (1c), it shows two sets of Fast Fourier Transform peaks and domain walls formed by kinks in the real space, indicating a pinning mode. At low densities (n<1), holes resemble a conventional generalized Wigner crystal but deviate from potential minima due to competitive Coulomb repulsion.