Quantum Café: Mitchell Luskin

Title: Physics and Math at the Moiré Scale

Abstract: The incommensurate stacking of multilayered two-dimensional materials has become an active experimental method to investigate physical properties and a challenging problem from a theoretical perspective. The configuration space is a natural description of such incommensurate layered materials and gives an exact formulation of electronic properties such as the density of states and Kubo optical conductivity. Our configuration space approach can model heterostructures of N layers (such as twisted trilayer graphene) for which there does not exist a 2D periodic structure by reformulating the incommensurate structure in the 2(N-1) dimensional configuration space. The Bistritzer-MacDonald (BM) model captures the electronic properties of twisted bilayer graphene (TBG) in the low energy, continuum limit. We will present theoretical and computational results that estimate the error and guide the development of more accurate continuum models.

Mitchell Luskin’s early work developed methods to model and compute the properties of materials with structural phase transitions, microstructure, and defects. Subsequent work developed and improved hybrid atomistic-to-continuum coupling methods and accelerated molecular dynamics. Luskin’s recent work has focused on the development of mathematical foundations and computational methods for 2D van der Waals heterostructures.

Luskin has been an assistant professor at the University of Michigan, a professor of applied mathematics at Caltech, and a full professor of mathematics at the University of Minnesota. He has also been a Radcliffe Fellow at Harvard University, Distinguished Romberg Fellow at the University of Heidelberg, and a Simons Fellow in Mathematics.