Kondo quantum criticality of magnetic adatoms in graphene

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as TK∝|J-Jc|1/3 near the critical coupling Jc, and the local spin is effectively screened by a super-Ohmic bath. For this class, the RKKY interaction decays spatially with a fast power law ∼1/R7. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.