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ABSTRACT: The quantum Hall effect in graphene is regarded to be involving half-integer
topological numbers associated with the massless Dirac particle, this is
usually not apparent due to the doubling of the Dirac cones. Here we
theoretically consider two classes of lattice models in which we manipulate the
Dirac cones with either (a) two Dirac points that have mutually different
energies, or (b) multiple Dirac cones having different Fermi velocities. We
have shown, with an explicit calculation of the topological (Chern) number for
case (a) and with an adiabatic argument for case (b) that the results are
consistent with the picture that a single Dirac fermion contributes the
half-odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) to the Hall
conductivity when the Fermi energy traverses the Landau levels.
Journal of Physics Conference Series 09/2010; 334(1).