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Paramagnetic impurities in a quantum spin-liquid can result in Kondo effectswith highly unusual properties. We have studied the effect of locallyexchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaevmodel in its gapless spin-liquid phase. The (impurity) scaling equations arefound to be insensitive to the sign of the coupling. The weak and strongcoupling fixed points are stable, with the latter corresponding to anoninteracting vacancy and an interacting, spin-1 defect for theantiferromagnetic and ferromagnetic cases respectively. The ground state in thestrong coupling limit in both cases has a nontrivial topology associated with afinite Z2 flux at the impurity site. For the antiferromagnetic case, thisresult can be obtained straightforwardly owing to the integrability of theKitaev model with a vacancy. The strong-coupling limit of the ferromagneticcase is however nonintegrable, and we address this problem throughexact-diagonalization calculations with finite Kitaev fragments. Our exactdiagonalization calculations indicate that that the weak to strong couplingtransition and the topological phase transition occur rather close to eachother and are possibly coincident. We also find an intriguing similaritybetween the magnetic response of the defect and the impurity susceptibility inthe two-channel Kondo problem.

A Kondo route to spin inhomogeneities in the honeycomb Kitaev model