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

Abstract

The strong time-reversal symmetric (TRS) topological insulator (TI) 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.

16 pages, 2 figures. Final minor corrections

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Cited by in corpus (12)

• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• The quest for Casimir repulsion between Chern-Simons surfaces
• Fractional Quantum Hall Effect in Weyl Semimetals
• Parity anomaly in four dimensions
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Functional Approach to Electrodynamics of Media
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Three-dimensional Topological Insulators and Bosonization
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Topological order in interacting semimetals
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• Capacitive scheme to detect the topological magnetoelectric effect