  We study the Kondo effect of spin-1/2 magnetic impurities in gapped Z2 spin
liquids on two-dimensional lattices. We find that if the impurity is placed at
a high-symmetry location, a nontrivial spinon fractionalization class of the
impurity site symmetry group will necessarily lead to a non-Kramers doublet in
the Kondo screening regime, protected by associated crystalline symmetries.
This is in sharp contrast to a featureless screening phase in the usual Kondo
effect. We demonstrate this symmetry-protected topological degeneracy by an
exactly solvable model and by the large-N theory. Based on this effect, we
discuss how thermodynamic measurements in the limit of dilute magnetic
impurities can be used to detect symmetry fractionalization in gapped Z2 spin
liquids.
