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

Abstract

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.

4 pages, 5 figures; v2: introduction expanded, data for Gaussian model extended to larger system sizes to further demonstrate single parameter scaling

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