Optical Properties of Massive Topological Dirac Semimetals

Most crystalline materials can be approximated as infinitely periodic systems. Our group investigates these lattice structures using a tight-binding model approach, wherein electrons occupy discrete lattice sites and are allowed to “hop” between neighboring sites. 

We explore a model for a 2D massless Dirac fermion on the square lattice.  Upon inclusion of a mass term, the system transitions from a topological semimetal to a topological insulator with a quantized Hall conductance proportional to the band structure’s Chern number. Moreover, we investigated a ribbon of this lattice and analyzed its bulk and edge states, calculating the probability of finding an electron at a certain location on the lattice when a certain electronic eigenstate is occupied.