Thin film topological insulators: where do we stand and where are we headed?

About a decade ago, a little after graphene was discovered, a few theoretical physicists proposed that all solids can be grouped into different classes according to their band structure topologies: depending on which group of the topological families the solid belongs to, it is supposed to carry distinct electronic properties. This notion of topology applied to the band structure of materials gave rise to the birth of topological materials as a new paradigm of condensed matter physics. In particular, according to these theories, all insulators can be grouped into either of the two material classes: topological vs. trivial insulators. The conventional insulators we know are all trivial insulators but several materials such as Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ were proposed and later confirmed to be topological insulators (TIs), which are supposed to be insulating in the bulk but guaranteed to be metallic on their surfaces. Because of the strongly mathematical nature of the concept of topology, once the notion of topology started being applied to material systems, numerous theoretical proposals for various exotic functionalities have emerged. Nevertheless, only a very small set of those proposals have been realized, mostly due to various defect problems. In this talk, I will show that some of these defect problems can be effectively overcome through ingenious thin film engineering schemes, and that mastering these defects reveals a number of hidden properties of topolgical insulators including quantum Hall effects, quantum Faraday/Kerr rotations, and topological phase transitions.