Multichannel topological Kondo effect

TL;DR

This paper introduces a multichannel topological Kondo model, explores its fixed points, and predicts observable signatures such as conductance and impurity entropy, revealing potential for realizing Fibonacci anyons.

Contribution

It generalizes the topological Kondo effect to multiple channels, analyzes fixed points, and connects the model to experimental observables and anyon realization.

Findings

Stable intermediate fixed point for N=2 with Fibonacci anyon implications

Mapping of N=2, M=4 case to conventional 4-channel Kondo model

Full crossover function for conductance in large-N limit

Abstract

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 $SO(M)$. The impurity spin stems from the non-local 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 4-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 cross over function describing the temperature-dependent conductance.