Mathematical modeling and numerical simulation of 2D materials
2D materials such as graphene have fascinating electronic and optical properties. Multilayer 2D materials are obtained by stacking several layers of possibly different 2D materials. Their study is one of the current hot topics in physics and materials science. The numerical simulation of such systems is made difficult by incommensurabilities originating from lattice mismatches and twisting angles. In this talk, I will first present the most common framework, based on Kubo formula, for deriving the frequency-dependent electrical conductivity tensor of a given material from its molecular structure. For periodic systems (perfect crystals), Bloch theory allows one to numerically compute the conductivity from Kubo formula in an efficient way. The situation is much more involved for aperiodic systems such as incommensurate multilayer 2D materials. However, it can be handled by relying on tools from non-commutative geometry introduced in the 80's and 90's by Jean Bellissard and co-workers following ideas of Alain Connes.