Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators

Heinrich-Gregor Zirnstein and Bernd Rosenow
Phys. Rev. B 88, 085105 – Published 5 August 2013

Abstract

The strong time-reversal symmetric topological insulator in three space dimensions features gapless surface states in the form of massless Dirac fermions. We study these surface states with the method of bosonization, and find that the resulting bosonic theory has a topological contribution due to the parity anomaly of the surface Dirac fermions. We argue that the presence of a quantum anomaly is, in fact, the main reason for the existence of a surface state, by the principle that anomalies of a surface and bulk must cancel. Inspecting other classes of topological insulators, we argue that this principle holds in general. Moving beyond purely topological considerations, we incorporate the dynamics of the surface electron states into the bosonic theory. Additionally, we discuss the thermodynamics of the bosonic theory and propose a representation of the surface Dirac fermions in terms of the bosonic fields.

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  • Received 28 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.085105

©2013 American Physical Society

Authors & Affiliations

Heinrich-Gregor Zirnstein and Bernd Rosenow

  • Institut für Theoretische Physik, Universität Leipzig, D-04103 Leipzig, Germany

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Issue

Vol. 88, Iss. 8 — 15 August 2013

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