Multichannel charge Kondo effect and non-Fermi-liquid fixed points in conventional and topological superconductor islands

Abstract

We study multiterminal Majorana and conventional superconducting islands in the vicinity of the charge degeneracy point using bosonization and the numerical renormalization group. Both models map to the multichannel charge Kondo problem, but for noninteracting normal leads they flow to different non-Fermi-liquid fixed points at low temperatures. We compare and contrast both cases by numerically obtaining the full crossover to the low-temperature regime, and we predict distinctive transport signatures. The differences between the two types of islands result from a crucial distinction between charge-$2e$ and charge-$e$ transfer in the conventional and topological case, respectively. In the conventional case, our results establish $s$-wave islands as a platform to study the intermediate multichannel Kondo fixed point. In the topological setup, the crossover temperature to non-Fermi-liquid behavior is relatively high as it is proportional to the level broadening, and the transport results are not sensitive to channel coupling anisotropy, moving away from the charge degeneracy point or including a small Majorana hybridization, which makes our proposal experimentally feasible.