Topology of Disconnected Elementary Band Representations

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Topology of Disconnected Elementary Band Representations

Jennifer Cano, Barry Bradlyn, Zhijun Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. Andrei Bernevig

Phys. Rev. Lett. 120, 266401 – Published 27 June 2018

Abstract

Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples—one each in a symmorphic and a nonsymmorphic space group—of elementary band representations realized with an energy gap. In doing so, we explicitly construct a counterexample to a claim by Michel and Zak that single-valued elementary band representations in nonsymmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are nontrivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the “Wilson Hamiltonian” and a bent- $Z_{2}$ index.

Received 17 January 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.266401

Physics Subject Headings (PhySH)

Topological phases of matter

Honeycomb lattice Topological insulators Topological materials

Lattice models in condensed matter Symmetries in condensed matter Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jennifer Cano¹, Barry Bradlyn¹, Zhijun Wang², L. Elcoro³, M. G. Vergniory^4,5, C. Felser⁶, M. I. Aroyo³, and B. Andrei Bernevig^2,4,7,*

¹Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
²Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
³Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
⁴Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
⁵Department of Applied Physics II, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain and Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
⁶Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
⁷Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France, Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France, and LPTMS, CNRS (UMR 8626), Université Paris-Saclay, 15 rue Georges Clémenceau, 91405 Orsay, France