Analytical and numerical study of uncorrelated disorder on a honeycomb lattice

• Main Authors: Lee, Kean Loon, Grémaud, Benoît, Miniatura, Christian, Delande, Dominique
• Other Authors: Institute of Advanced Studies
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/101624; http://hdl.handle.net/10220/18746
• Institution: Nanyang Technological University

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.