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 Ec; the wires are coupled to normal-metal leads via tunnel junctions. Using a combination of analytical and numerical techniques we calculate the average charge on the island as well as non-local conductance matrix as a function of a p-wave pairing gap ΔP, charging energy Ec and dimensionless junction conductances gi. 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. Specifically, in contrast with conventional (s-wave) mesoscopic superconducting islands, we find that Coulomb blockade effects are suppressed in Majorana islands regardless of the ratio Ec/ΔP or the magnitude of the conductances gi. We also discuss our findings in relation to the so-called topological Kondo effect.
