Electron localization in disordered graphene for nanoscale lattice sizes: multifractal properties of the wavefunctions

An analysis of the electron localization properties in doped graphene is performed by carrying out a numerical multifractal analysis for finite systems of a size smaller than the possible localization length. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions present a multifractal behavior for systems up to 20 nm. Such multifractality is preserved even for next-to-nearest neighbor hopping interaction, which needs to be taken into account if a comparison with experimental results is desired. 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 one to conclude that in the split-band limit, where impurities act as vacancies, the system can be described well by a chiral orthogonal symmetry class.