Exact real space formulation and efficient computation of the electronic properties of 2D heterostructures

  We will present a novel real space approach to the formulation and computation of the mechanical and electronic properties of twisted bilayer graphene and other 2D moiré materials that gives an exact representation of the electronic density of states, the Kubo formula for optical conductivity, and other electronic properties for the true aperiodic structure of 2D moiré materials without a supercell or continuum approximation. We will present efficient computational methods to approximate this formulation that exploits the locality of the hopping functions and the kernel polynomial method.