The Alexander-Anderson problem for two atoms adsorbed on graphene

The Green’s functions for the Alexander-Anderson problem have been obtained using the previously proposed model density of states for graphene. Both the ferromagnetic and antiferromagnetic dimers have been considered. It has been shown that, in order to describe the density of states of the dimer adatom, the density of states of the isolated adatom with two positions of the gravity center of the quasi-level shifted in opposite directions can be used. It has been demonstrated that the approximate method of obtaining the Green’s function of the dimer proposed by us previously and consisting in that the Green’s function of the adatom rather than that of the atom is taken as the seed function gives the same result as the Alexander-Anderson approach. The dependences of the indirect interaction of dimer adatoms on the problem parameters have been evaluated in the limit of low energies.