The Good, the Bad and the Ugly: Surfaces and Interfaces of Topological Insulators

Identification of topological nature of electronic matter has led to remarkable theoretical and experimental advances in large part because topological arguments do not depend on the specific details of the material, and hence their predictions are general and universal.  In practice, however, separating the universal from the non-universal properties of topological systems is not always easy. I will focus on the class of compounds called topological insulators (Tis) that have metallic surfaces despite not conducting current in the bulk, and start with a non-technical review of the relevant concepts and introduction to the basic physics. I will then discuss heterostructures containing these materials, which constitute the next frontier in the effort to incorporate topological matter into functional electronic devices. I will show that the properties of the interface states appearing at the planar boundary between a TI and a conventional semiconductor are different from those of the well-studied surface states at vacuum termination.  The interface states are generally non-helical and have anisotropic dispersion. I will analyze the university of the properties of the interface states, and experimental signatures of the predicted behavior. Finally, I will demonstrate the consequences of our findings for hybrid superconductor-topological insulator proximity structures.