AI Article Synopsis
- The text discusses a new method for constructing and classifying topological states that are protected by both onsite and spatial symmetry groups.
- It introduces the concept of "topological crystals," where these states are arranged in a specific spatial configuration without open edges, making them stable under symmetry transformations.
- The authors provide a detailed enumeration of all unique types of topological crystals for certain electronic insulators, leading to a comprehensive classification of topological crystalline insulators.
Article 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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6920025 | PMC |
| http://dx.doi.org/10.1126/sciadv.aax2007 | DOI Listing |
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