Electron localization in disordered graphene: multifractal properties of the wavefunctions

• Main Authors: Barrios-Vargas, J. E, Naumis, Gerardo G
• Format: Journal Article
• Language: English
• Published: 27-06-2013
• Subjects: Physics - Disordered Systems and Neural Networks; Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.1306.6665

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.