Mathematical and Physical Aspects of Topologically Protected States

Mathematical Modeling and Numerical Analysis for Incommensurate 2D Materials

Mitchell Luskin

University of Minnesota


Stacking a few layers of 2D materials such as graphene and molybdenum disulfide, for example, opens the possibility to tune the electronic and optical properties of 2D materials. One of the main issues encountered in the mathematical and computational modeling of layered 2D materials is that lattice mismatch and rotations between the layers destroys the periodic character of the system. Basic concepts like the electronic density of states and the Kubo-Greenwood formulas for transport properties will be presented in the incommensurate setting. New computational approaches will be discussed and the validity and efficiency of these approximations will be examined from mathematical and numerical analysis perspectives with insight from topological concepts.