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We study a Majorana island coupled to a bulk superconductor via a Josephsonjunction and to multiple external normal leads. In the absence of the Josephsoncoupling, the system displays a topological Kondo state, which had been largelystudied recently. However, we find that this state is unstable even to smallJosephson coupling, which instead leads at low temperature $T$ to a new fixedpoint. Most interesting is the case of three external leads, forming a minimalelectronic realization of the long sought two-channel Kondo effect. While the$T=0$ conductance corresponds to simple resonant Andreev reflection, theleading $T$ dependence forms an experimental fingerprint for non-Fermi liquidproperties.

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