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 non-local conductance matrix as a function of a p-wave pairing gap ${\Delta }_P$, 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 $E_C/{\Delta }_P$ or the magnitude of the conductances $g_i$. We also discuss our findings in relation to the so-called topological Kondo effect.

27 pages, 6 figures. Submitted version

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• Embedded Majorana Islands
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• A mesoscopic device for a realization of the Topological Kondo effect