Engineering of impurity bands with Chern Numbers

Abstract

Recently, there have been studies on p-wave superconductor system designed with a lattice of impurity over its surface. They result in non-trivial topological phases with high-values of Chern Numbers. The present thesis investigates a similar model starting with a 3D strong Topological Insulator - experimentally established. Focusing on one surface, first we place a ferromagnetic material to create an energy gap on the surface spectrum, then we display a square rarefied lattice of magnetic impurities. That is a two-bands model and we derive for it an effective Hamiltonian. Calculating the Chern Numbers of the in-gap bands structure and studying the surface energy spectrum, we find the setting responds like a Chern Insulator. Finally, comparing the spectrum energy initial condition of our model to the p-wave superconductor one, we mention the next improvements to eventually reach high-values of Chern Numbers.