Signatures of topological ground state degeneracy in Majorana islands

Abstract

We consider a mesoscopic superconducting island hosting multiple pairs of Majorana zero-energy modes. The Majorana island consists of multiple p-wave wires connected together by a trivial (s-wave) superconducting backbone and is characterized by an overall charging energy E_{C}; the wires are coupled to normal-metal leads via tunnel junctions. We calculate the average charge on the island as well as nonlocal conductance matrix as a function of a p-wave pairing gap Δ_{P}, charging energy E_{C}, and dimensionless junction conductances g_{i}. We find that the presence of a topological ground-state degeneracy in the island dramatically enhances charge fluctuations and leads to the suppression of Coulomb blockade effects. In contrast with conventional (s-wave) mesoscopic superconducting islands, we find that Coulomb blockade oscillations of conductance are suppressed in Majorana islands regardless of the ratio E_{C}/Δ_{P} or the magnitude of the conductances g_{i}. We also discuss our findings in relation to the so-called topological Kondo effect.