Topological states from topological crystals

Song, Zhida; Huang, Sheng-Jie; Qi, Yang; Fang, Chen; Hermele, Michael

doi:10.1126/sciadv.aax2007

Title: Topological states from topological crystals

Journal Article · 18 December 2019 · Science Advances

DOI: https://doi.org/10.1126/sciadv.aax2007 · OSTI ID:1626023

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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
Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter
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)
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)
Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter

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.

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Research Organization:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0014415; 2016YFA0302400; 2016YFA0300600; 11674370; XXH13506-202; 2015CB921700

OSTI ID:: 1626023

Journal Information:: Science Advances, Vol. 5, Issue 12; ISSN 2375-2548

Publisher:: AAASCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 39 works

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