Topological insulator and the θ vacuum in a system without boundaries

Abstract

In this paper we address two questions concerning the effective action of a topological insulator in one- and three-dimensional space without boundaries, such as a torus. The first is whether a uniform θ term with θ=π is generated for a strong topological insulator. The second is whether such a term has observable consequences in the bulk. The answers to both questions are positive, but the observability in three dimensions vanishes for infinite system size. © 2011 American Physical Society.