Spectral approach to transport in the 2D honeycomb lattice with substitutional disorder

TL;DR

This study uses a spectral numerical approach to analyze how substitutional disorder affects electron transport in a 2D honeycomb lattice, revealing a transition from extended to localized states at a critical doping level.

Contribution

It introduces a spectral method to study transport in disordered 2D honeycomb lattices and identifies a critical doping threshold for localization transition.

Findings

Existence of extended states at nonzero disorder levels.

Localization transition occurs at doping concentration above 0.3%.

Results align with experimental metal-insulator transition in doped graphene.

Abstract

The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the quantum percolation problem, characterized by an Anderson-type Hamiltonian. In our simulations, substitutional disorder (or doping) is represented by a modified bimodal probability distribution of the on-site energies. The results indicate the existence of extended energy states for nonzero disorder and the emergence of a transition towards localized behavior for critical doping concentration n_D>0.3%, in agreement with the experimentally observed metal-to-insulator transition in graphene sheet doped with hydrogen.