Two-Channel Kondo Physics in a Majorana Island Coupled to a Josephson Junction

TL;DR

This paper investigates a Majorana island coupled to a superconductor and normal leads, revealing a transition from a topological Kondo state to a non-Fermi liquid two-channel Kondo effect with distinctive temperature-dependent conductance.

Contribution

It demonstrates the instability of the topological Kondo state under Josephson coupling and identifies a minimal setup for realizing the two-channel Kondo effect.

Findings

Topological Kondo state is unstable with Josephson coupling.

Low-temperature conductance shows non-Fermi liquid behavior.

Three-lead setup realizes the two-channel Kondo effect.

Abstract

We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant Andreev reflection, the leading $T$ dependence forms an experimental fingerprint for non-Fermi liquid properties.