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

TL;DR

This paper provides a straightforward proof that the axion term in the electromagnetic response of three-dimensional topological insulators is quantized and invariant under shifts of 2π, confirming a key theoretical property.

Contribution

It offers the first simple, physically motivated proof of the quantization and periodicity of the axion action in topological insulators, based on wavefunction single-valuedness.

Findings

Proof of axion action quantization on periodic space-time

Confirmation of invariance under  heta + 2\u03c0 shifts

Assumption only of single-valued electron wavefunctions

Abstract

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.