Metropolis Sampling of Moiré Superlattices of Transition Metal Dichalcogenide Models

We introduce a classical model that enables the investigation of the effects of interlayer coupling parameters on moiré structures in twisted bilayer van der Waals (vdWs) materials. Metropolis sampling with nontraditional boundary conditions and machine learning techniques are used to produce and analyze results. This model employs a parametrization of the Stillinger-Weber potential appropriate for describing the intralayer interactions of transition metal dichalcogenides (TMDCs), and a simple Lennard-Jones potential for the interlayer interactions. To generate equilibrium configurations, we use Metropolis Monte Carlo with unique fluctuating boundary conditions to minimize boundary effects. These methods allow us to recreate superlattices seen in experiment and ab initio calculations.1 Additionally, we sample different values of the van der Waals radii of the interlayer interaction σMo–S′ and σS–S′ to explore how competition of interaction affects morphology of periodic domains seen in reconstructed moiré TMDCs. We then employ simple machine learning procedures to classify and analyze a variety of simulated structures to further extract model parameters that drive domain formation. Finally, we apply our method to the simulation of heterobilayers with different lattice constants, which are difficult to accommodate via experiment or first-principles calculations. In so doing we find both continuous and abrupt differences in moiré superlattice spacing. These generic models, with appropriate boundary conditions, hold great potential for exploring moiré and other reconfigurable atomic scale phenomena in quantum materials.