Topological phases protected by point group symmetry
We consider symmetryprotected 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 lowerdimensional topological phases with onsite symmetry and that they can be constructed as stacks and arrays of these lowerdimensional 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 threedimensional states. We classify bosonic pgSPT phases and fermionic topological crystalline superconductors with Z ^{P} _{2} (reflection) symmetry, electronic topological crystalline insulators (TCIs) with U(1)×Z ^{P} _{2} symmetry, and bosonic pgSPT phases with C _{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 _{8} × Z _{2} classification, where the Z _{8} corresponds to known states obtained from noninteracting electrons, and the Z _{2} corresponds to a “strongly correlated” TCI that requires strong interactions in the bulk. Lastly, our approach may also point themore »
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[2]}
 Univ. of Colorado, Boulder, CO (United States); Univ. Complutense, Madrid (Spain)
 Univ. of Colorado, Boulder, CO (United States)
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Publication Date:
 Grant/Contract Number:
 SC0014415; SC0010526
 Type:
 Published Article
 Journal Name:
 Physical Review. X
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 21603308
 Publisher:
 American Physical Society
 Research Org:
 Univ. of Colorado, Boulder, CO (United States); Massachusetts Institute of Technology, Cambridge, MA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1344619
 Alternate Identifier(s):
 OSTI ID: 1367191
Song, Hao, Huang, Sheng Jie, Fu, Liang, and Hermele, Michael. Topological phases protected by point group symmetry. United States: N. p.,
Web. doi:10.1103/PhysRevX.7.011020.
Song, Hao, Huang, Sheng Jie, Fu, Liang, & Hermele, Michael. Topological phases protected by point group symmetry. United States. doi:10.1103/PhysRevX.7.011020.
Song, Hao, Huang, Sheng Jie, Fu, Liang, and Hermele, Michael. 2017.
"Topological phases protected by point group symmetry". United States.
doi:10.1103/PhysRevX.7.011020.
@article{osti_1344619,
title = {Topological phases protected by point group symmetry},
author = {Song, Hao and Huang, Sheng Jie and Fu, Liang and Hermele, Michael},
abstractNote = {We consider symmetryprotected 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 lowerdimensional topological phases with onsite symmetry and that they can be constructed as stacks and arrays of these lowerdimensional 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 threedimensional 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 symmetryenriched topological phases with crystalline point group symmetry.},
doi = {10.1103/PhysRevX.7.011020},
journal = {Physical Review. X},
number = 1,
volume = 7,
place = {United States},
year = {2017},
month = {2}
}
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