We analyze the full transport statistics of graphene with smooth disorder at low dopings. First, we consider the case of one-dimensional (1D) disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength, and correlation length) in an identical fashion for large enough systems. In the case of two-dimensional (2D) disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is universal. Specific universal values are given for the Fano factor, which is smaller than the pseudodiffusive value of ballistic graphene $(F=1∕3)$ both for 1D $(F\approx 0.243)$ and 2D $(F\approx 0.295)$ disorders. On the other hand, conductivity in wide samples is shown to grow without saturation as $\sqrt{L}$ and $\log L$ with system length $L$ in the 1D and 2D cases, respectively.

• Received 27 June 2007

DOI:https://doi.org/10.1103/PhysRevB.76.195445