Distant-Neighbor Hopping in Graphene and Haldane Models

Doru Sticlet (1, 2, 3) , Frédéric Piéchon (1)

1 LPS - Laboratoire de Physique des Solides
2 LOMA - Laboratoire Ondes et Matière d'Aquitaine
3 MPI-PKS - Max-Planck-Institut für Physik komplexer Systeme

Large Chern number phases in a Haldane model become possible if there is a multiplication of Dirac points in the underlying graphene model. This is realized by considering long-distance hopping integrals. Through variation of these integrals, it is possible to arrive at supermerging band touchings, which up to N7 graphene are unique in parameter space. They result from the synchronized motion of all supplementary Dirac points into the regular +/-K points of graphene. The energy dispersion power law is usually larger than the topological charge associated with them. Moreover, adding distant-neighbor hoppings in the Haldane mass allows one to sweep large Chern number phases in the topological insulator.

Mots clés: Quantum phase transitions; Electronic structure of graphene; Electron states at surfaces and interfaces; Phases: geometric - dynamic or topological

Domaines: Matière Condensée [cond-mat]

Doru Sticlet, Frédéric Piéchon. Distant-Neighbor Hopping in Graphene and Haldane Models. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2013, 87 (11), pp.115402 (1-11). ⟨10.1103/PhysRevB.87.115402⟩. ⟨hal-00811626⟩