Adsorption on graphene with vacancy-type defects: A model approach

The influence of graphene lattice defects on the adsorption properties of graphene has been considered. The adsorption properties have been investigated in the framework of the Anderson model. The disorder of the graphene crystal lattice has been analyzed using the $T$-matrix approximation. It has been found that the characteristic energy levels of defects are located near the Dirac point ($\pm$1 eV), because the most significant distortions of the spectrum due to the presence of defects in the graphene crystal lattice are observed in the vicinity of this point. Analytical expressions for the density of states of disordered graphene and atoms adsorbed on it have been obtained. A numerical calculation of the charge transfer in the considered system has been carried out. The obtained values of the charge transfer are in good agreement with the results of other studies, where the charge transfer was calculated using the experimental data and the density functional theory method. In the absence of defects, the presented results are well consistent with the results obtained within the $M$-model of adsorption (Davydov model). An approximation for the density of states of disordered graphene and the shift function of an adsorbed atom has been proposed. This approximation allows one to obtain analytical expressions for the charge transfer, energy of adsorption, and dipole moment.