Topological view on magnetic adatoms in graphene

We study theoretically the physical properties of a magnetic impurity in graphene. The theory is based on the Anderson model with a very strong Coulomb interaction on the impurity. We start from the slave-boson method and introduce a topological picture consisting of a degree of a map and a winding number (WN) to analyze the phase shift and the occupation on the impurity. The occupation is linked to the WN. For a generic normal metal we find a fractional WN. In contrast, the winding is accelerated by the relativistic dispersion of graphene at half-filling, in which case an integer occupation is realized. We show that the renormalization that shifts the impurity level is insufficient to invert the sign of the energy level. Consequently, the state at half-filling is stable unless a gate voltage is tuned such that the Fermi level touches the edge of the broadened impurity level. Only in this case is the zero field susceptibility finite and shows a pronounced peak structure when scanning the gate voltage.