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Topological Insulators from Group Cohomology

Author(s): Alexandradinata, A; Wang, Zhijun; Bernevig, Bogdan A.

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dc.contributor.authorAlexandradinata, A-
dc.contributor.authorWang, Zhijun-
dc.contributor.authorBernevig, Bogdan A.-
dc.identifier.citationAlexandradinata, A, Wang, Zhijun, Bernevig, B Andrei. (2016). Topological Insulators from Group Cohomology. PHYSICAL REVIEW X, 6 (10.1103/PhysRevX.6.021008en_US
dc.description.abstractWe 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.en_US
dc.relation.ispartofPHYSICAL REVIEW Xen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleTopological Insulators from Group Cohomologyen_US
dc.typeJournal Articleen_US

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