Finding Dirac Cones in Two Dimensional Artificial Lattices

Abstract

The focus of this thesis lies on finding Dirac cones in band structures of two dimensional artificial lattices. These special band crossing points (BCP's) indicate interesting electronic properties of the material. In two dimensional systems, the symmetry of the lattice determines whether BCP's occur. Graphene, with its hexagonal lattice structure, is the best known 2D material that contains Dirac cones. Our goal is here to look for Dirac cones in two dimensional artificial square lattices. Using the symmetries of the square, we try to find Dirac cones in the band structure. To create these lattices artificially, we use the nearly free electron model as an approximation to the tight binding model describing a crystal. This approximation is valid for low energy ranges. Using three different types of lattices, each defined by a different potential landscape, we find Dirac cones emerging in two of them.