Universal scaling of current fluctuations in disordered graphene

Abstract

We analyze the full transport statistics of graphene with smooth disorder at\nlow dopings. First we consider the case of 1D disorder for which the\ntransmission probability distribution is given analytically in terms of the\ngraphene-specific mean free path. All current cumulants are shown to scale with\nsystem parameters (doping, size, disorder strength and correlation length) in\nan identical fashion for large enough systems. In the case of 2D disorder,\nnumerical evidence is given for the same kind of identical scaling of all\ncurrent cumulants, so that the ratio of any two such cumulants is universal.\nSpecific universal values are given for the Fano factor, which is smaller than\nthe pseudodiffusive value of ballistic graphene (F=1/3) both for 1D (F=0.243)\nand 2D (F=0.295) disorder. On the other hand, conductivity in wide samples is\nshown to grow without saturation as \\sqrt{L} and Log L with system length L in\nthe 1D and 2D cases respectively.\n