Topological Insulator and the $\theta$-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 $\theta$-term with $\theta =\pi$ 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 dimension vanishes for infinite system size.

9 pages, 4 figures

References in corpus (4)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Orbital magnetoelectric coupling in band insulators
• Theory of orbital magnetoelectric response
• Witten effect in a crystalline topological insulator

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• Topological order and Berry connection for the Maxwell Vacuum on a four-torus
• Topological Casimir effect in a quantum LC circuit: real-time dynamics
• Static Electric Field in a 1D Systems without Boundaries