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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.

SUBMITTER: Song Z

PROVIDER: S-EPMC6920025 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

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Topological states from topological crystals.

Song Zhida Z Huang Sheng-Jie SJ Qi Yang Y Fang Chen C Hermele Michael M

Science advances 20191218 12

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 grou ...[more]

PMID: 31897424

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