Resonant scattering due to adatoms in graphene: Top, bridge, and hollow positions

We present a theoretical study of resonance characteristics in graphene from adatoms with $s$ or $p_z$ character binding in top, bridge, and hollow positions. The adatoms are described by two tight-binding parameters: onsite energy and hybridization strength. We explore a wide range of different magnitudes of these parameters by employing T-matrix calculations in the single adatom limit and by tight-binding supercell calculations for dilute adatom coverage. We calculate the density of states and the momentum relaxation rate and extract the resonance level and resonance width. Top position with large hybridization strength or, equivalently, small onsite energy, induces resonances close to zero energy. Bridge position, compared to top, is more sensitive to variation in the orbital tight-binding parameters. Resonances within the experimentally relevant energy window are found mainly for bridge adatoms with negative onsite energies. The effect of resonances from top and bridge position on the density of states and momentum relaxation rate is comparable and both positions give rise to power-law decay of the resonant state in graphene. Hollow position with $s$ orbital character is affected from destructive interference which is seen from very narrow resonance peaks in the density of states and momentum relaxation rate. The resonant state shows no clear tendency to power-law decay around the impurity and its magnitude decreases strongly with lowering the adatom content in the supercell calculations. This is in contrast to top and bridge position. We conclude our study with a comparison to models of point-like vacancies and strong midgap scatterers. The latter model gives rise to significantly higher momentum relaxation rates than caused by single adatoms.