Analytical and numerical study of uncorrelated disorder on a honeycomb lattice

Abstract

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.

arXiv comment19 pages, 25 figures

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• Dynamics of localized waves in 1D random potentials: statistical theory of the coherent forward scattering peak
• Obtaining localization properties efficiently using the Kubo-Greenwood formalism
• Non-equilibrium Green's function study of magneto-conductance features and oscillations in clean and disordered nanowires
• Effects of disorder and contacts on transport through graphene nanoribbons
• Localisation and finite-size effects in graphene flakes
• Anderson localization induced by structural disorder
• Strong-coupling perturbative study of the disordered Hubbard model on honeycomb lattice
• Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations
• Momentum Signatures of Site Percolation in Disordered 2D Ferromagnets