One-Parameter Scaling at the Dirac Point in Graphene

J. H. Bardarson, J. Tworzydło, P. W. Brouwer, and C. W. J. Beenakker
Phys. Rev. Lett. 99, 106801 – Published 5 September 2007

Abstract

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)=dlnσ/dlnL. 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.

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  • Received 7 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.106801

©2007 American Physical Society

Authors & Affiliations

J. H. Bardarson1, J. Tworzydło2, P. W. Brouwer3,4, and C. W. J. Beenakker1

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
  • 2Institute of Theoretical Physics, Warsaw University, Hoża 69, 00–681 Warsaw, Poland
  • 3Physics Department, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilans-Universität, 80333 Munich, Germany
  • 4Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

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Issue

Vol. 99, Iss. 10 — 7 September 2007

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