Violation of the single-parameter scaling hypothesis in disordered graphene nanoribbons

A numerical statistical analysis of the conductance g distribution function in disordered graphene nanoribbons is presented. Calculations are performed within the nonequilibrium Green’s Function formalism. We have checked that the conductance variance in these quasi one-dimensional systems scales linearly with the average of the logarithm of g, i.e., 2=A-ln g+B in the localization regime. However, the slope A is not a constant as the disorder degree varies in any region of the energy spectrum, i.e., the single parameters scaling hypothesis is not verified. Our results stimulate further investigations in order to categorize the conductance fluctuations on the basis of the band structure and/or lattice topology of the system in study.