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Kondo effect in monolayer and bilayer graphene: physical realizations of the multi-channel Kondo models

We perform a general group-theoretical study of the Kondo problem in monolayer and bilayer graphene around the charge neutrality point. Utilizing the group representation theory, we derive from symmetry considerations a family of the Kondo models for all symmetric placements with either 3- or 6-fold rotational axis of an impurity atom in an arbitrary orbital state. We find six possible classes of the partially anisotropic four-channel Kondo model. As the key result, we argue several possibilities to realize the regime of the dominant channel-symmetric two-channel Kondo effect, protected by the local symmetry and specifics of the graphene band structure. Our findings open prospects for the observation of the rich multi-channel Kondo physics in graphene and the associated non-Fermi-liquid behavior.