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

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

2010-06-17

arxiv.org/abs/1006.3355v2

Phys. Rev. B 82, 233103 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form '\theta E dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under '\theta -> \theta +2\pi'. 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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