Many-terminal Majorana island: From topological to multichannel Kondo model

We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-1/2 multichannel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter K in the leads that is effectively doubled. For strong interactions K=1/2, the intermediate fixed point of the standard multichannel Kondo model is exactly recovered. It evolves with K and connects to strong coupling in the noninteracting case K=1, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multichannel Kondo state.