Applied Math Seminar: Modeling electronic transport properties in incommensurate 2D multilayer materials

Seminar | March 7 | 4-5 p.m. | 740 Evans Hall

 Paul Cazeaux, University of Kansas

 Department of Mathematics

The recent discovery of a whole family of two-dimensional crystalline materials such as graphene, hexagonal boron nitride (h-BN) and many others leads to study the properties of their combinations, particularly by stacking a number of layers vertically. Such structures are generally non-periodic, with interesting geometric properties such as moiré effects. We first recall the usual description for electronic structure and conduction phenomena in periodic as well as disordered systems, using quantum models of tight-binding type. We show how a unified framework, formulated by Bellissard et al. in the context of noncommutative geometry to model disordered systems, extends to non-periodic systems with multiple layers and allows to write an explicit formula for their macroscopic electrical conductivity. This abstract framework surprisingly leads to a new type of numerical scheme going beyond traditional methods.