Past Event: Oden Institute Seminar

Mathematics and Physics at the Moiré Scale

Mitchell Luskin, School of Mathematics, University of Minnesota

Abstract

Stacking a few layers of 2D materials such as graphene or molybdenum disulfide at controlled twist angle has opened the possibility of tuning the electronic properties of 2D materials.  One of the main issues encountered in the mathematical and computational modeling of twisted 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system.

We have developed a novel variational model for elastic relaxation and a new mathematical formulation for the electronic density of states, band structure, and transport for the incommensurate Hamiltonian.  New computational approaches will be presented, and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives.

Biography

Mitchell Luskin’s early work developed mathematical formulations and analysis to model and compute the properties of materials with defects and microstructure.  Subsequent work proposed and analyzed 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 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. He is a fellow of SIAM and AMS.