Impurity States in Chern Insulators

Abstract

This thesis examines in what ways the introduction of an impurity in an insulator (with and without topological order) affects the manifestation of in-gap bound states. This is done by constructing a model for the Chern insulator, adding an impurity in the form of a chemical potential, and studying how this alters the behavior of the system's electrons. Although this has been investigated analytically earlier this year \cite{Leiden}, numerical evidence was not yet available. The results of this research show that in the topological insulator an additional in-gap bound state around the impurity emerges. Meanwhile, in-gap bound states remain generically absent in the case of the trivial insulator. This confirms the predictions of \cite{Leiden}.