Analytical and numerical study of uncorrelated disorder on a honeycomb lattice

TL;DR

This paper investigates how uncorrelated disorder affects electronic properties on a honeycomb lattice using numerical and analytical methods, confirming the one-parameter scaling theory but highlighting limitations of the self-consistent localization theory.

Contribution

It provides a detailed comparison of recursive Green's function and self-consistent Born approximation methods for disordered honeycomb lattices, validating the scaling theory of localization.

Findings

Excellent agreement between methods for single-particle properties.

Localization lengths collapse onto a single curve across sizes and energies.

Self-consistent localization theory quantitatively fails to match numerical localization lengths.

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.