Topological insulators from group cohomology

A. Alexandradinata, Zhijun Wang, B. Andrei Bernevig

Research output: Contribution to journalArticle

68 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number021008
JournalPhysical Review X
Volume6
Issue number2
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Topological insulators from group cohomology'. Together they form a unique fingerprint.

  • Cite this