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Title: Topological Phases Protected by Point Group Symmetry

Journal Article · · Physical Review. X
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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 ZP2 (reflection) symmetry, electronic topological crystalline insulators (TCIs) with U(1)×ZP2 symmetry, and bosonic pgSPT phases with C2v 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 Z8 × Z2 classification, where the Z8 corresponds to known states obtained from noninteracting electrons, and the Z2 corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Lastly, our approach may also point the way toward a general theory of symmetry-enriched topological phases with crystalline point group symmetry.

Research Organization:
Univ. of Colorado, Boulder, CO (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0014415; SC0010526
OSTI ID:
1344619
Alternate ID(s):
OSTI ID: 1367191
Journal Information:
Physical Review. X, Journal Name: Physical Review. X Vol. 7 Journal Issue: 1; ISSN 2160-3308
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 121 works
Citation information provided by
Web of Science

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