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 $beta(sigma)=dlnsigma/dln L$. 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.