Hourglass fermions

Zhijun Wang, A. Alexandradinata, R. J. Cava, B. Andrei Bernevig

Research output: Contribution to journalArticle

172 Scopus citations

Abstract

Spatial symmetries in crystals may be distinguished by whether they preserve the spatial origin. Here we study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these non-symmorphic symmetries protect an exotic surface fermion whose dispersion relation is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These 'hourglass' fermions are formed in the large-gap insulators, KHgX (X = As, Sb, Bi), which we propose as the first material class whose band topology relies on non-symmorphic symmetries. Besides the hourglass fermion, another surface of KHgX manifests a three-dimensional generalization of the quantum spin Hall effect, which has previously been observed only in two-dimensional crystals. To describe the bulk topology of non-symmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our non-trivial topology originates from an inversion of the rotational quantum numbers, which we propose as a criterion in the search for topological materials.

Original languageEnglish (US)
Pages (from-to)189-194
Number of pages6
JournalNature
Volume532
Issue number7598
DOIs
StatePublished - Apr 13 2016

All Science Journal Classification (ASJC) codes

  • General

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