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

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.

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