Analytical and numerical study of uncorrelated disorder on a honeycomb   lattice
  We consider a tight-binding model on the regular honeycomb lattice with uncorrelated on-site disorder. We use two independent methods (recursive Green's function and self-consistent Born approximation) to extract the scattering mean free path, the scattering mean free time, the density of states and the localization length as a function of the disorder strength. The two methods give excellent quantitative agreement for these single-particle properties. Furthermore, a finite-size scaling analysis reveals that all localization lengths for different lattice sizes and different energies (including the energy at the Dirac points) collapse onto a single curve, in agreement with the one-parameter scaling theory of localization. The predictions of the self-consistent theory of localization however fail to quantitatively reproduce these numerically-extracted localization lengths. 
Kean Loon Lee, Beno\^it Gr\'emaud, Christian Miniatura, Dominique   Delande
cond-mat.dis-nn cond-mat.quant-gas quant-ph