Surface States in Topological Insulators and Superconductors: Discovery and Recent Results

Bulk Topological Insulators are a new phase of electronic matter which realizes a non-quantum-Hall-like topological state in the bulk matter and unlike the quantum Hall liquids can be turned into superconductors. In this Lecture, I will first review the basic theory of topological matter and experimental probes that reveal topological order. I will discuss experimental results that demonstrate the fundamental properties of topological insulators such as spin-momentum locking, non-trivial Berry’s phases, mirror Chern number, absence of backscattering or no U-turn rule, protection by time-reversal symmetry and the existence of room temperature topological order (at the level of M.Z.H and C.L. Kane, Rev. of Mod. Phys., 82, 3045 (2010)). I will then discuss the possible exotic roles of broken symmetry phases such as superconductivity and magnetism in doped topological insulators and their potential device applications in connection to our recent results as well as outline the emerging research frontiers of the field as a whole.