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 sigma(xy) and the longitudinal conductance sigma(xx) are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at v = 0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between +/-E(c), 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 similar to 1.0 and similar to 7/3.