Multiscale models for moiré materials

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 initial discovery of superconductivity 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, I will present an efficient and accurate multiscale framework based on first principles. Using this framework, I study the electronic structures, mechanical relaxation, and phonon properties of complex vdW heterostructures and interpret experimental observations. I will also discuss the surprising extension of the multiscale framework to aperiodic systems beyond the quantum mechanical scale, particularly focusing on understanding the topology of ocean waves and fusion plasmas.