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 a vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function beta(sigma)=dlnsigma/dlnL. 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 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.
Bardarson
J H
JH
Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Tworzydło
J
J
Brouwer
P W
PW
Beenakker
C W J
CW