Multiscale Models for Incommensurate Layered Two-dimensional Materials

Abstract

Manipulating the twist angle or lattice mismatch in stacks of multilayered two-dimensional (2D) materials, referred to as van der Waals (vdW) heterostructures, introduces a long-wavelength moiré potential that fundamentally alters the physical properties of the constituent materials. Following the discovery of superconductivity and unconventional correlated insulating states in single-twist moiré systems, forays into moiré of moiré vdW heterostructures, such as twisted trilayer graphene with two independent twist angles, have led to observations of novel correlated states. These complex multilayered heterostructures exhibit length scales that are generally orders of magnitude longer than the bilayer moiré length, and they are incommensurate even in the continuum limit. To overcome these computational challenges, we present an efficient and accurate multiscale framework based on first principles. Using this framework, we study the electronic structures, mechanical re- laxation, and phonon properties of complex vdW heterostructures and help interpret experimental observations. We also introduce a machine learning-based approach to solving many-body lattice models, which may serve as a starting point toward solving the effective theory for these complex 2D materials.