Langevin Dynamics/Monte Carlo Simulations of Structural and Dielectric Modulations of Moire Materials

We have developed a fast and flexible computational scheme to calculate the complex valued, frequency dependent dielectric function of correlated materials. We use an atomistic bilayer model that includes phenomenological bond and bond-angle interactions, as well as empirical inter-layer interactions for layered heterostructures. Such systems are then subject to an oscillating external electric field representing an AFM tip. We simulate systems of unit cells with fluctuating boundary conditions using Langevin dynamics. We show how our methodology couples with Monte Carlo methods to give us nanoscale insight into both the dielectric modulation and structural transformation of Moiré patterned two-dimensional transition metal dichalcogenides. We show the formation of stress domains that vary widely in shape and configuration with regard to inter-layer couplings. Such patterns are then keenly compared to relevant experimental results on the same systems.