We propose to use residual anyons of the overscreened Kondo effect for topological quantum computation. A superconducting proximity gap of $\mathrm{\Delta }<T_K$ can be utilized to isolate the anyon from the continuum of excitations and stabilize the nontrivial fixed point. We use weak-coupling renormalization group, dynamical large-N technique, and bosonization to show that the residual entropy of multichannel Kondo impurities survives in a superconductor. We find that while (in agreement with recent numerical studies) the nontrivial fixed point is unstable against intrachannel pairing, it is robust in the presence of a finite interchannel pairing. Based on this observation, we suggest a superconducting charge Kondo setup for isolating and detecting the Majorana fermion in the two-channel Kondo system.

• Received 24 November 2019
• Revised 20 May 2020
• Accepted 20 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.235131