Topological Phases Protected by Point Group Symmetry
Name
PhysRevX.7.011020.pdf
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694.61 KB
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Author(s)
Song, Hao
Huang, Sheng-Jie
Fu, Liang
Hermele, Michael
Date Issued
February 2017
Journal
Physical Review X
Publisher
American Physical Society
Citation
Song, Hao et al. “Topological Phases Protected by Point Group Symmetry.” Physical Review X 7.1 (2017): n. pag. © 2017 American Physical Society.
Version
Final published version
Abstract
We consider symmetry-protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry and that they can be constructed as stacks and arrays of these lower-dimensional states. This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, which can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimensions. We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with Z[subscript 2][superscript P] (reflection) symmetry, electronic topological crystalline insulators (TCIs) with U(1)×Z[subscript 2][superscript P] symmetry, and bosonic pgSPT phases with C[subscript 2v] symmetry, which is generated by two perpendicular mirror reflections. We also study surface properties, with a focus on gapped, topologically ordered surface states. For electronic TCIs, we find a Z[subscript 8]×Z[subscript 2] classification, where the Z[subscript 8] corresponds to known states obtained from noninteracting electrons, and the Z[subscript 2] corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Our approach may also point the way toward a general theory of symmetry-enriched topological phases with crystalline point group symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevX.7.011020
