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

We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap ?. We find that the low-energy spectrum in the limit ?->0 actually does not correspond to the spectrum strictly at ?=0. In particular, in the two-channel Kondo model, the ?->0 ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at ?=0. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of ? tends toward a finite and universal value when ?->0, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by ??0. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite ?: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.