Quantum Hall effect of Haldane model under magnetic field

Haldane model can realize the anomalous quantum Hall effect (QHE) without Landau levels (LLs) and serves as a prototype of the quantum spin Hall effect. In this paper, we study the QHE of Haldane model under magnetic field with magnitude such that the magnetic flux in a plaquette is commensurate with the lattice structure. First, we show the origin of unconventional QHE in graphene and point out a general rule for the Hall step of Dirac fermions, which strongly depends on the valley degeneracy of each LL. Second, we study the conductance around the neutral point which lies in the gap given by continuous bands, revealing the competition between periodic magnetic flux and uniform magnetic field. Moreover, the redistribution behavior of Chern number is investigated. We find that besides the staggered magnetic flux, the next-nearest-neighbor hopping can also induce the redistribution. We also study the QHE of the extended Haldane model on a square lattice. Copyright (C) EPLA,