6 pi Josephson Effect in Majorana Box Devices

We study Majorana devices featuring a competition between superconductivity and multichannel Kondo physics. Our proposal extends previous work on single-channel Kondo systems to a topologically nontrivial setting of a non-Fermi liquid type, where topological superconductor wires (with gap Delta) represent leads tunnel coupled to a Coulomb-blockaded Majorana box. On the box, a spin degree of freedom with Kondo temperature T-K is nonlocally defined in terms of Majorana states. For Delta >> T-K, the destruction of Kondo screening by superconductivity implies a 4 pi-periodic Josephson current-phase relation. Using a strong-coupling analysis in the opposite regime Delta << TK, we find a 6 pi-periodic Josephson relation for three leads, with critical current I-c approximate to e Delta(2)/hT(K), corresponding to the transfer of fractionalized charges e*=2e/3.