期刊
PHYSICAL REVIEW X
卷 6, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.6.021008
关键词
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资金
- NSF CAREER [DMR-095242]
- ARO MURI [W911NF-12-1-0461]
- NSF-MRSEC [DMR-1420541]
- Packard Foundation
- Keck grant [25812-G0001-10006242-101]
- Schmidt fund [23800-E2359-FB625]
- Yale Prize Fellowship
- [ONR - N00014-11-1-0635]
We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as piecewise topological, in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.
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