Axion field theory approach and the classification of interacting topological superconductors

Yingfei Gu; Xiao-Liang Qi

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arXiv · 1512.04919

Axion field theory approach and the classification of interacting topological superconductors

Yingfei Gu·Xiao-Liang Qi

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Abstract

In this paper, we discuss the topological classification of time-reversal invariant topological superconductors. Based on the axion field theory developed in a previous work (Phys. Rev. B ${\bf 87}$ 134519 (2013)), we show how a simple quantum anomaly in vortex-crossing process predicts a $\mathbb{Z}_{16}$ classification of interacting topological superconductors, in consistency with other approaches. We also provide a general definition of the quantum anomaly and a general geometric argument that explains the $\mathbb{Z}_{16}$ on more general grounds. Furthermore, we generalize our approach to all $4n$ dimensions (with $n$ an integer), and compare our results with other approaches to the topological classification.

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Yingfei Gu, Xiao-Liang Qi. 2015-12-15. Axion field theory approach and the classification of interacting topological superconductors. https://arxiv.org/abs/1512.04919

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