Modeling incommensurate trilayer van der Waals heterostructures

Mitchell Luskin
University of Minnesota

Abstract: The incommensurate stacking of multilayered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. We first present a multiscale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles. The configuration space of twisted trilayers graphene is generally a four-dimensional torus without a two- dimensional moiré description because of the incommensurate coupling of two bilayer moiré patterns, and the relaxation patterns of twisted trilayer graphene are consequently “moiré of moiré.” We will show that the Euler-Lagrange partial differential equation for the relaxation energy is not elliptic and gives a small divisor problem for a possibly hypoelliptic operator. We next introduce twisted trilayer graphene (tTLG) with two independent twist angles as an ideal system for the precise tuning of the electronic interlayer coupling to maximize the effect of correlated behaviors. We present a general low-energy electronic structure model for any pair of twist angles and show that the basis of the model has infinite dimensions even at a finite energy cutoff.

Biography: Mitchell Luskin is a professor of mathematics at the University of Minnesota who is working to develop computational methods to accurately and efficiently simulate complex physical systems at large length and time scales. His interests include methods that couple atomistic to continuum models and accelerated molecular dynamics. Prof. Luskin received a BS in mathematics from Yale College and a PhD in mathematics from the University of Chicago. He has recently been a distinguished Romberg Guest Professor at the University of Heidelberg and a visiting scholar at Pembroke College Cambridge. He is a fellow of the American Mathematical Society and the Society for Industrial and Applied Mathematics.