Theory of Fano resonances in graphene: The influence of orbital and structural symmetries on STM spectra

We theoretically investigate Fano factors arising in local spectroscopy of impurity resonances in graphene. It is demonstrated that Fano line shapes can strongly differ from the antiresonances usually found on metal surfaces. Graphene's highly symmetric Fermi points make this effect particularly sensitive to the detailed atomistic structure and orbital symmetries of the impurity. After a model discussion based on an Anderson impurity coupled to an electron bath with linearly vanishing density of states, we present first-principles calculations of Co adatoms on graphene. For Co above the center of a graphene hexagon, we find that the two-dimensional E-1 representation made of d(xz), d(yz) orbitals is likely responsible for the hybridization and ultimately Kondo screening for cobalt on graphene. Anomalously large Fano q factors depending strongly on the orbitals involved are obtained. For a resonant s-wave impurity, a similarly strong adsorption site dependence of the q factor is demonstrated. These anomalies are striking examples of quantum-mechanical interference related to the Berry phase inherent to the graphene band structure.