Dissipation and criticality in the lowest Landau level of graphene

Abstract

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 plateau-like feature centered at =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.