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Title: Topological states from topological crystals

Abstract

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5]
+ Show Author Affiliations
  1. Chinese Academy of Sciences (CAS), Beijing (China). Beijing National Research Center for Condensed Matter Physics and Institute of Physics; Princeton Univ., NJ (United States). Dept. of Physics
  2. Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter
  3. Fudan Univ., Shanghai (China). Center for Field Theory and Particle Physics, Dept. of Physics; Fudan Univ., Shanghai (China). State Key Laboratory of Surface Physics; Collaborative Innovation Center of Advanced Microstructures, Nanjing (China)
  4. Chinese Academy of Sciences (CAS), Beijing (China). Beijing National Research Center for Condensed Matter Physics and Institute of Physics; CAS Center for Excellence in Topological Quantum Computation, Beijing (China)
  5. Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1626023
Grant/Contract Number:  
SC0014415; 2016YFA0302400; 2016YFA0300600; 11674370; XXH13506-202; 2015CB921700
Resource Type:
Accepted Manuscript
Journal Name:
Science Advances
Additional Journal Information:
Journal Volume: 5; Journal Issue: 12; Journal ID: ISSN 2375-2548
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Science & Technology - Other Topics

Citation Formats

Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, and Hermele, Michael. Topological states from topological crystals. United States: N. p., 2019. Web. doi:10.1126/sciadv.aax2007.
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Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, & Hermele, Michael. Topological states from topological crystals. United States. https://doi.org/10.1126/sciadv.aax2007
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Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, and Hermele, Michael. Wed . "Topological states from topological crystals". United States. https://doi.org/10.1126/sciadv.aax2007. https://www.osti.gov/servlets/purl/1626023.
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@article{osti_1626023,
title = {Topological states from topological crystals},
author = {Song, Zhida and Huang, Sheng-Jie and Qi, Yang and Fang, Chen and Hermele, Michael},
abstractNote = {We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.},
doi = {10.1126/sciadv.aax2007},
journal = {Science Advances},
number = 12,
volume = 5,
place = {United States},
year = {2019},
month = {12}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1126/sciadv.aax2007
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