2007/05/31 by Jens H. Bardarson, J. H. Bardarson, J. Tworzydło +3 · 340 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Graphene #Graphene research and applications #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Scaling limit #Scattering #Sigma #Statistical physics #Surface and Thin Film Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.99.106801
published in Physical Review Letters 99(10), 106801 (American Physical Society) · 4 pages, 5 figures; v2: introduction expanded, data for Gaussian model extended to larger system sizes to further demonstrate single parameter scaling
arxiv created 2007/06/27 · openalex publication_date 2007/09/05 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.