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.