Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators

Sungjoon Hong; Liang Fu

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arXiv · 1707.02594

Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators

Sungjoon Hong·Liang Fu

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Abstract

We present microscopic Hamiltonians that gap the Dirac fermions on the surface of topological crystalline insulators (TCIs) protected by reflection symmetry and create symmetry-preserving states with Abelian topological orders. For TCIs with $n = 2$ copies of surface Dirac fermions, we find a fermionic $\mathbb{Z}_4$ topological order with charge-spin self duality and with a novel symmetry action on the anyons, whereby reflections with respect to two parallel planes act differently. We also analyze TCIs with $n = 1$ and $4$ copies of Dirac fermions, which taken together covers every nontrivial case in the $\mathbb{Z}_8 \oplus \mathbb{Z}_2$ classification of interacting TCIs. Our work reveals a fundamental difference between reflection and charge-conjugation-time-reversal symmetry anomalies.

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Sungjoon Hong, Liang Fu. 2017-07-09. Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators. https://arxiv.org/abs/1707.02594

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