The ℤ2 invariant of two-dimensional topological insulators

Abstract

A time-reversal invariant topological insulator either has no topologically protected edge states, or one pair of such edge states. Thus, its bulk topological invariant is either 0 or 1: it is a (Formula presented.) number. Although obtaining a single yes/no answer might seem easier than the calculation of a Chern number, the (Formula presented.) invariant is notoriously difficult to calculate. In this chapter we detail a way to calculate it that follows the same logic as before for the Chern number.