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Topological view on magnetic adatoms in graphene

We study theoretically the physical properties of a magnetic impurity in graphene. Within the Anderson model for 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 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 leading to an integer occupation. We show that the renormalization parameter 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 the zero field susceptibility is finite and shows a pronounced peak structure with the gate voltage.