Demonstration of one-parameter scaling at the Dirac point in graphene

We numerically calculate the conductivity $\sigma$ of an undoped graphene sheet (size $L$) in the limit of vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function $\beta(\sigma)=d\ln\sigma/d\ln L$. Contrary to a recent prediction, the scaling flow has no fixed point ($\beta>0$) for conductivities up to and beyond the symplectic metal-insulator transition. Instead, the data supports an alternative scaling flow for which the conductivity at the Dirac point increases logarithmically with sample size in the absence of intervalley scattering -- without reaching a scale-invariant limit.Comment: 4 pages, 5 figures; v2: introduction expanded, data for Gaussian model extended to larger system sizes to further demonstrate single parameter scalin

Impurity-assisted tunneling in graphene

The electric conductance of a strip of undoped graphene increases in the presence of a disorder potential, which is smooth on atomic scales. The phenomenon is attributed to impurity-assisted resonant tunneling of massless Dirac fermions. Employing the transfer matrix approach we demonstrate the resonant character of the conductivity enhancement in the presence of a single impurity. We also calculate the two-terminal conductivity for the model with one-dimensional fluctuations of disorder potential by a mapping onto a problem of Anderson localization.Comment: 6 pages, 3 figures, final version, typos corrected, references adde