Electron localization in disordered graphene: multifractal properties of the wavefunctions

TL;DR

This study investigates electron localization in doped graphene using multifractal analysis, revealing complex wavefunction behavior and challenging traditional views on two-dimensional localization.

Contribution

It demonstrates that electron wavefunctions in doped graphene exhibit multifractality, even with second neighbor interactions, and links these properties to symmetry classes and localization theories.

Findings

Wavefunctions are multifractal near the Dirac point.

Multifractality persists with second neighbor interactions.

Localization behavior challenges conventional 2D Anderson localization.

Abstract

An analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions present a multifractal behavior. Such multifractality is preserved even for second neighbor interaction, which needs to be taken into account if a comparison is desired with experimental results. States close to the Dirac point have a wider multifractal character than those far from this point as the impurity concentration is increased. The analysis of the results allows to conclude that in the split-band limit, where impurities act as vacancies, the system can be well described by a chiral orthogonal symmetry class, with a singularity spectrum transition approaching freezing as disorder increases. This also suggests that in doped graphene, localization is in contrast with the conventional picture of Anderson localization in two dimensions, showing also that the common belief of the absence of quantum percolation in two dimensional systems needs to be revised.