Title: Computational Non-Commutative Geometry for Multilayer 2D Materials
Abstract: Stacks of 2D one-atom thick crystalline layers form a new example of aperiodic systems. These structures have a lot to offer, with the possibility of combining the properties of highly disparate materials such as graphene, hexagonal boron nitride and many others, and interesting geometrical properties such as Moire patterns.I will first recall standard models for disordered systems, such as doped semiconductors (meso-scale disorder) or amorphous materials (atom-scale disorder). I will show how a unified description, formulated in the framework of non-commutative geometry introduced by Bellissard to model general disordered systems, extends to multi-layered nonperiodic systems.I will present a tight-binding model which allows to write down an explicit formula for the macroscopic electrical conductivity of incommensurate multilayer 2D materials. This abstract framework also leads surprinsingly to a new kind of numerical scheme beyond the scope of traditional methods.