Bachelor's defense: Mads Kruuse

Title: Graphene as a Two-Dimensional Topological Insulator and the Quantum Anomalous Hall Effect

In this talk I will introduce the Haldane Hamiltonian, which historically is the first known model of the Chern insulator. I start by introducing a simple tight-binding Hamiltonian and after a brief discussion of symmetries I will introduce the Haldane model. A discussion of the Berry phase is given and how this relates to the Chern number. This number is what characterizes the different phases of the Haldane model and it is argued that the Hall conductance is directly related to this quantity. Subsequently the phase diagram for the Haldane model is discussed and finally the existence of edge modes is shown for a semi-infinite system. It is argued that the appearence of chiral edge modes is a consequence of the non-trivial phase of the Haldane model known as the bulk edge correspondance.