Tight-binding model for adatoms on graphene: Analytical density of states, spectral function, and induced magnetic moment

In the limit of low adatom concentration, we obtain exact analytic expressions for the local and total density of states (LDOS, TDOS) for a tight-binding model of adatoms on graphene. The model is not limited to nearest-neighbor hopping but can include hopping between carbon atoms at any separation. We also find an analytical expression for the spectral function $A(\mathbf{k},E)$ of an electron of Bloch vector $\mathbf{k}$ and energy $E$ on the graphene lattice, to first order in the adatom concentration. We treat the electron-electron interaction by including a Hubbard term on the adatom, which we solve within a mean-field approximation. For finite Hubbard $U$, we find the spin-polarized LDOS, TDOS, and spectral function self-consistently. For any choice of parameters of the tight-binding model within mean-field theory, we find a critical value of $U$ above which a moment develops on the adatom. Preliminary calculations also indicate that this moment can be switched on and off by varying the Fermi energy. For most choices of parameters, we find a substantial charge transfer from the adatom to the graphene host.