Bulk Topological Insulators and Superconductors: Discovery and the Frontier

  M. Zahid Hasan  
Princeton University

While most known phases of matter are characterized by broken symmetries, the discovery of quantum Hall effects (1980s) revealed that there exists an organizational principle based on topology rather than broken symmetry. In the past few years, theory and experiments have suggested that new types of topological states of matter exist in certain insulators without any applied magnetic field. These topological insulators are characterized by a full band gap in their bulk and gap-less conducting edge or surface states protected by time-reversal symmetry. Unlike the quantum Hall systems, the topological insulators can be doped into superconductors and magnets revealing the interplay between topological order and broken symmetry order. In this talk, I will briefly review the basic theory and highlight the experimental developments in topological insulators. I will then conclude by drawing connections b etween the emergent novel physics and their potential applications.