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.