Multichannel Kondo Effect in gapful Superconducting Leads

In the conventional Kondo effect, the quantum impurity interacts with bulk gapless conformal degrees of freedom, leading to its screening, described by the strong coupling Fermi liquid fixed point. In the multichannel effect, the impurity is overscreened and described by a non-Fermi-liquid fixed point with non-trivial critical exponents. Using the Bethe Ansatz, we demonstrate that the multichannel Kondo effect persists even when the bulk degrees of freedom are gapped. Specifically, we consider a single spin-1/2 impurity, isotropically coupled to n one-dimensional superconducting leads with a dynamically generated spin gap. Depending on the relative strengths of the bulk and boundary couplings four distinct regimes arise: an overscreened Kondo phase, a zero-mode phase, a Yu–Shiba–Rusinov (YSR) phase, and a local-moment phase with an unscreened impurity. We find that in each phase, the Hilbert space splits into different excitation towers constructed over different basis states. Analyzing the renormalization-group flow, excitation spectrum, and temperature-dependent impurity entropy, we show that this splitting has a profound effect on the impurity thermodynamic properties. While in the Kondo regime, the impurity entropy decreases monotonically with temperature, in the YSR and local-moment regimes, it exhibits non-monotonic behavior due to competing boundary and bulk effects. Remarkably, even in the presence of a bulk mass gap, the low-energy theory in the Kondo phase flows to the same SU(2)_n Wess–Zumino–Witten fixed point as in the gapless multichannel Kondo model.