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.
Highlights
The effect of quantum fluctuations in mesoscopic islands of superconducting metals has been extensively studied in the last two decades [1,2,3,4,5,6,7]
When such an island is coupled to normal leads, one can show that the topological ground-state degeneracy manifests itself in a number of different ways: The superconducting charge fluctuations are enhanced, suppressing Coulomb blockade effect; the conductance Gi j between leads i and j reaches a universal value Gi= j = 2e2/(Mh) at T = 0 independent of the applied gate voltage
We assume that L is much larger than the p-wave coherence length so we can ignore the hybridization of the Majorana states through the central segment
Summary
The effect of quantum fluctuations in mesoscopic islands of superconducting metals has been extensively studied in the last two decades [1,2,3,4,5,6,7]. Away from charge degeneracy points (known as the valley), tunneling of Cooper pairs across the superconducting island is suppressed at low temperatures T , i.e., G ∝ T 2 [10,11] This conclusion holds for any number of normal-metal (noninteracting) leads connected to the island. [26,27,28,29] that the remaining topological ground-state degeneracy can be used for quantum information processing When such an island is coupled to normal leads, one can show that the topological ground-state degeneracy manifests itself in a number of different ways: The superconducting charge fluctuations are enhanced, suppressing Coulomb blockade effect; the conductance Gi j between leads i and j reaches a universal value Gi= j = 2e2/(Mh) at T = 0 independent of the applied gate voltage.
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