Archive ouverte HAL – Topological proximity effects in a Haldane graphene bilayer system

Peng Cheng 1 Philipp W. KleinKirill Plekhanov 2, 3 Klaus Sengstock 4 Monika AidelsburgerChristof Weitenberg 5 Karyn Le Hur 2 Philipp KleinKaryn Le Hur 2

Peng Cheng, Philipp W. Klein, Kirill Plekhanov, Klaus Sengstock, Monika Aidelsburger, et al.. Topological proximity effects in a Haldane graphene bilayer system. Physical Review B : Condensed matter and materials physics, American Physical Society, 2019, 100 (8), ⟨10.1103/PhysRevB.100.081107⟩. ⟨hal-02291915⟩

We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

  • 1. DALEMBERT – Institut Jean Le Rond d’Alembert
  • 2. CPHT – Centre de Physique Théorique [Palaiseau]
  • 3. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 4. Zentrum für Optische Quantentechnologien
  • 5. MPQ – Max-Planck-Institut für Quantenoptik

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