General Theory of Topological Insulators

 

Shou-Cheng Zhang, Stanford University

 

Currently there exist two apparently-different theoretical descriptions of topological insulators. In the case of non-interacting fermions, topological invariants can be defined over discrete time-reversal invariant momenta. On the other hand, we showed sometime ago that time-reversal invariant topological insulators can be generally defined by the effective topological field theory with a quantized theta coefficient, which can only take values of 0 or pi. The latter theory is generally valid for an arbitrary interacting system and the quantization of the theta invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the theta invariant can be expressed as an integral over the entire three dimensional Brillouin zone. In this talk, I will explain the topological field theory description of topological insulators and its consequences. I will then show the complete equivalence between the integral and the discrete invariants of the topological insulator, thus establishing a general theory of topological insulators. Other related theoretical ideas and generalizations will also be discussed.