Interaction-Induced Renormalization of Tunneling into Multiple Majorana End States of a Topological Superconducting Wire

We investigate a system of multiple Majorana states at the end of a topological superconducting wire coupled to a normal lead. For a minimum of three Majorana fermions at the interface, we find nontrivial renormalization physics. Interface tunneling processes can be classified in terms of spin-1/2 and spin-3/2 irreducible representations of the SU(2) group. We show that the renormalization of the tunneling amplitudes belonging to different representations is completely different in that one type is suppressed, whereas the other is enhanced, depending on the sign of the interaction coupling. This results in distinct temperature dependencies of the tunneling current through the interface and different spin polarizations of this current.