Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance σxy and the longitudinal conductance σxx are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at ν=0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between ±Ec, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be 2.47±0.04. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between ∼1.0 and ∼7/3.