A Coulomb blockaded $M$-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group $\mathrm{SO}(M)$. The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated $N$-channel generalization of the topological Kondo model. Starting from the simplest case $N=2$, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the $N=2$ model. We also map the case $N=2$, $M=4$ to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-$N$ limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. In the large-$N$ limit, we evaluate the full crossover function describing the temperature-dependent conductance.

• Received 27 July 2022
• Revised 10 November 2022
• Accepted 11 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.066302