Topology of Disconnected Elementary Band Representations

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

Research output: Contribution to journalArticlepeer-review


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-Z2 index.

Original languageEnglish (US)
Article number266401
JournalPhysical review letters
Issue number26
StatePublished - Jun 27 2018
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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