One-Parameter Scaling at the Dirac Point in Graphene

We numerically calculate the conductivity σ of an undoped graphene sheet (size L) in the limit of a vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function β(σ)=dln⁡σ/dln⁡L. Contrary to a recent prediction, the scaling flow has no fixed point (β>0) for conductivities up to and beyond the symplectic metal-insulator transition. Instead, the data support 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.