Quantization and $2\pi$ Periodicity of the Axion Action in Topological Insulators

Abstract

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form 'θE dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under 'θ-> θ+2π'. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space-time, assuming only that the vector potential is consistent with single-valuedness of the electron wavefunctions in the underlying insulator.

4 pages, 1 figure, version2 (section on axion action quantization of non-periodic systems added)

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Cited by in corpus (22)

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• Dynamical axion state with hidden pseudospin Chern numbers in MnBi${}_2$Te${}_4$-based heterostructures
• Models of three-dimensional fractional topological insulators
• Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI
• Electromagnetic effects induced by time-dependent axion field
• Walker-Wang models and axion electrodynamics
• Axion crystals
• Fractionalized topological insulators from frustrated spin models in three dimensions
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Magnetoelectric effect in topological insulator films beyond the linear response regime
• High spin axion insulator
• Van der Waals torque and force between anisotropic topological insulator slabs
• Axion instability and non-linear electromagnetic effect
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Remarks on the static potential in theories with Lorentz violation terms
• Dirac Fermions and Topological Phases in Magnetic Topological Insulator Films
• Interactions and the Theta Term in One-Dimensional Gapped Systems
• Effective field theory of topological insulator and the Foldy-Wouthuysen transformation
• The magnetoelectric effect due to a semispherical capacitor surrounded by a spherical topologically insulating shell
• Remarks on a compact Abelian Higgs model