2007/06/30 by Pablo San-José, P. San-Jose, Elsa Prada +3 · 2 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Approx #Ballistic conduction #Combinatorics #Condensed matter physics #Conductance #Cumulant #Fano factor #Geometry #Graphene #Graphene research and applications #Low-power high-performance VLSI design #Mathematics #Mean free path #Nanopore and Nanochannel Transport Studies #Physics #Quantum mechanics #Saturation (graph theory) #Scaling #Statistical physics #Statistics #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.76.195445
published as Physical Review B 76, 195445 (2007) · 9 pages, 7 figures. Published version, includes corrected figure for Fano factor
openalex publication_date 2007/11/29 · arxiv created 2007/11/30 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the full transport statistics of graphene with smooth disorder at low dopings. First, we consider the case of one-dimensional (1D) disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength, and correlation length) in an identical fashion for large enough systems. In the case of two-dimensional (2D) disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is universal. Specific universal values are given for the Fano factor, which is smaller than the pseudodiffusive value of ballistic graphene (F=1∕3) both for 1D (F\ensuremath≈0.243) and 2D (F\ensuremath≈0.295) disorders. On the other hand, conductivity in wide samples is shown to grow without saturation as √(L) and log\phantom\rule0.2em0exL with system length L in the 1D and 2D cases, respectively.