Full counting statistics in disordered graphene at the Dirac point: From ballistics to diffusion

The full counting statistics of the charge transport through an undoped graphene sheet in the presence of smooth disorder is studied. At the Dirac point both in clean and diffusive limits, transport properties of a graphene sample are described by the universal Dorokhov distribution of transmission probabilities. In the crossover regime, deviations from universality occur which can be studied analytically both on ballistic and diffusive sides. In the ballistic regime, we use a diagrammatic technique with matrix Green’s functions. For a diffusive system, the sigma model is applied. Our results are in good agreement with recent numerical simulations of electron transport in disordered graphene.