Transport regimes in surface disordered graphene sheets

The conductance G of graphene stripes (of width W and length L) with surface disorder and near the Dirac point is investigated numerically. Incoherent metallic leads are attached to the sample ends across its width. In samples of W/L >= 1, the system behaves diffusively with G ->(2/pi)(W/L)x2e(2)/h, for L ->infinity, as found in the clean limit, although with a sharply reduced shape dependence. The conductance in elongated samples, L > W, decays exponentially with L, indicating localization. A similar behavior is found in clean elongated systems due to the existence of minigaps near the Dirac point. Average decay lengths are larger in the presence of disorder. A magnetic field does not appreciably change the conductance unless the flux per unit cell is significant. The distribution of conductances is almost flat between lower and upper cutoffs. Away from the Dirac point, we find the standard ballistic behavior characteristic of systems with rough edges.