Coulomb blockade of a nearly-open Majorana island
Dmitry I. Pikulin, Karsten Flensberg, Leonid I. Glazman, Manuel, Houzet, and Roman M. Lutchyn

TL;DR
This paper analyzes the Coulomb blockade effects in a nearly-open Majorana island, revealing how the modulation amplitude depends on reflection and energy parameters, bridging topological and conventional superconducting behaviors.
Contribution
It provides a detailed theoretical analysis of Coulomb blockade in Majorana islands with arbitrary junction transmission, highlighting the dependence on reflection coefficient and energy scales.
Findings
Modulation amplitude scales as √R for small R.
Amplitude dependence resembles that of a Cooper-pair box at larger R.
Crossover R value depends on energy ratios.
Abstract
We consider the ground-state energy and the spectrum of the low-energy excitations of a Majorana island formed of topological superconductors connected by a single-mode junction of arbitrary transmission. Coulomb blockade results in -periodic modulation of the energies with the gate-induced charge. We find the amplitude of modulation as a function of reflection coefficient . The amplitude scales as in the limit . At larger , the dependence of the amplitude on the Josephson and charging energies is similar to that of a conventional-superconductor Cooper-pair box. The crossover value of is small and depends on the ratio of the charging energy to superconducting gap.
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