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While the quantum Hall effect in graphene has been regarded as a realizationof the anomaly associated with the massless Dirac particle carrying half theusual topological integer, this is hidden due to the doubling of the Diraccones. In order to confirm the half-integer contribution from each Dirac cone,here we theoretically consider a lattice model in which the relative energybetween the two Dirac points is systematically shifted. With an explicitcalculation of the topological (Chern) number, we have demonstrated that eachDirac cone does indeed contribute to the Hall conductivity as the half oddinteger series (... -3/2, -1/2, 1/2, 3/2, ...) when the Fermi energy traversesthe (shifted sets of) Landau levels. The picture is also endorsed, via thebulk-edge correspondence, from the edge mode spectrum for the present model.

Half-integer contributions to the quantum Hall conductivity from single Dirac cones