Optical Properties of the α-T3 Semi-Dirac Model
Graphene is a two-dimensional honeycomb lattice structure composed of carbon. Single-layer graphene was first theorized in 1947, but was not observed experimentally until 2004. This discovery was awarded the Nobel Prize in physics in 2010. The honeycomb lattice structure of graphene can be used as a starting point to examine many other interesting models; two important examples include the dice (or T3) lattice and the α-T3 lattice, which interpolates between graphene and the dice lattice via a tunable parameter α. In this thesis the Kubo formula is used to calculate optical properties of a two-dimensional semi-Dirac α-T3 model, where the electron dispersion in momentum is linear (Dirac-like) in one direction and quadratic in the other. The frequency dependence of the longitudinal conductivity is found to be different for the x-direction versus the y-direction, providing characteristic signatures of the semi-Dirac behaviour.