  Paramagnetic impurities in a quantum spin-liquid can result in Kondo effects
with highly unusual properties. We have studied the effect of locally
exchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaev
model in its gapless spin-liquid phase. The (impurity) scaling equations are
found to be insensitive to the sign of the coupling. The weak and strong
coupling fixed points are stable, with the latter corresponding to a
noninteracting vacancy and an interacting, spin-1 defect for the
antiferromagnetic and ferromagnetic cases respectively. The ground state in the
strong coupling limit in both cases has a nontrivial topology associated with a
finite Z2 flux at the impurity site. For the antiferromagnetic case, this
result can be obtained straightforwardly owing to the integrability of the
Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic
case is however nonintegrable, and we address this problem through
exact-diagonalization calculations with finite Kitaev fragments. Our exact
diagonalization calculations indicate that that the weak to strong coupling
transition and the topological phase transition occur rather close to each
other and are possibly coincident. We also find an intriguing similarity
between the magnetic response of the defect and the impurity susceptibility in
the two-channel Kondo problem.
