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We study how the non-Fermi-liquid nature of the overscreened multi-channelKondo impurity model affects the response to a BCS pairing term that, in theabsence of the impurity, opens a gap $\Delta$. We find that non-Fermi liquidfeatures do persist even at finite $\Delta$: the local density of states lackscoherence peaks, the states in the continuum above the gap are unconventional,and the boundary entropy is a non-monotonic function of temperature. Even moresurprisingly, we also find that the low-energy spectrum in the limit $\Delta\to0$ actually does not correspond to the spectrum strictly at $\Delta=0$. Inparticular, the $\Delta\to 0$ ground state is an orbitally degeneratespin-singlet, while it is an orbital singlet with a residual spin degeneracy at$\Delta=0$. In addition, there are fractionalized spin-1/2 sub-gap excitationswhose energy in units of $\Delta$ tends towards a finite and universal valuewhen $\Delta\to 0$; as if the universality of the anomalous power-law exponentsthat characterise the overscreened Kondo effect turned into universal energyratios when the scale invariance is broken by $\Delta\not=0$. This intriguingphenomenon can be explained by the renormalisation flow towards theoverscreened fixed point and the gap cutting off the orthogonality catastrophesingularities.

Non-Fermi-liquid behavior in quantum impurity models with superconducting channels