Effect of Disorder on Transport in Graphene.pdf

Effect of Disorder on Transport in Graphene I. L. Aleiner1 and K. B. Efetov1,2, 3 1Physics Department, Columbia University, New York, NY 10027, USA 2 Theoretische Physik III, Ruhr-Universit¨at Bochum, 44780 Bochum, Germany 3L. D. Landau Institute for Theoretical Physics, 117940 Moscow, Russia (Dated: February 3, 2008) 6 Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic 0 renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve 0 renormalization group equations (RGEs) describing the system at such scales. At larger scales, we 2 derive a non-linear supermatrix σ-model completely describing localization and crossovers between l different ensembles. The parameters of this σ -model are determined by the solutions of the RGEs. u J PACS numbers: 73.63.-b,81.05.Uw, 72.15.Rn 7 ] ′ n Introduction– Dirac spectrum of the quasiparticles in where we use the fact the points K and K are connected n graphene confirmed by recent experiments [1–3] is a con- to each other by the time reversal symmetry