title: Hourglass fermions.
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.
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Zhijun
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.|Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
authors.forename: A
authors.initials: A
authors.lastname: Alexandradinata
authors.affiliation: Department of Chemistry, Princeton University, Princeton, New Jersey 08540, USA.
authors.forename: R J
authors.initials: RJ
authors.lastname: Cava
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: B Andrei
authors.initials: BA
authors.lastname: Bernevig