Magnetic adatoms on graphene in the Kondo regime: an Anderson model treatment

We study theoretically the Kondo effect for a magnetic adatom on graphene using the Anderson model.Upon obtaining the Green's function of the impurity to higher order contributions in the hybridization, we calculated analytically the selfenergy in the presence of strong correlations.It is found that the Kondo resonance takes place in a narrow energy range of the impurity level around the Fermi energy which can be tuned by a gate voltage.We show that this range is linear in the Fermi energy $|\mu|$ and is significantly narrower than in the case for a normal metal.The origin of this behavior is traced back to the inherent properties of graphene, especially its linear dispersion.The singularity in the full Green's function is also analyzed with the help of a transparent geometrical method.The relations between the various selfenergies and the implications for the experimental observations are discussed .