Archive ouverte HAL – Topology of Disconnected Elementary Band Representations

Jennifer Cano ¹ Barry Bradlyn ¹ Zhijun Wang ² L. Elcoro ³ M. g. Vergniory ³ C. Felser ⁴ M. i. Aroyo ³ B. Andrei Bernevig ^{5, 6, 7}

Physical Review Letters, American Physical Society, 2018, 120 (26), 〈10.1103/PhysRevLett.120.266401〉

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 non-symmorphic 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 non-symmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are non-trivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the « Wilson Hamiltonian » and a bent-Z2 index.

• 1. Princeton University, Princeton, NJ 08544, USA
• 2. Princeton University
• 3. University of the Basque Country – University of the Basque Country
• 4. CPfS – Max Planck Institute for Chemical Physics of Solids
• 5. DPPU – Department of Physics,Princeton University
• 6. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 7. LPA – Laboratoire Pierre Aigrain