期刊
SCIENCE ADVANCES
卷 5, 期 12, 页码 -出版社
AMER ASSOC ADVANCEMENT SCIENCE
DOI: 10.1126/sciadv.aax2007
关键词
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资金
- Ministry of Science and Technology of China under the Ministry of Science and Technology of China [2016YFA0302400, 2016YFA0300600]
- National Science Foundation of China [11874115, 11674370]
- Chinese Academy of Sciences [XXH13506-202]
- U.S. Department of Energy, Office of Science, Basic Energy Sciences (BES) [DE-SC0014415]
- Ministry of Science and Technology of China [2015CB921700]
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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