Coulomb blockade of a nearly-open Majorana island

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 $e$-periodic modulation of the energies with the gate-induced charge. We find the amplitude of modulation as a function of reflection coefficient ${\cal R}$. The amplitude scales as $\sqrt{\cal R}$ in the limit ${\cal R}\to 0$. At larger ${\cal R}$, 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 ${\cal R}$ is small and depends on the ratio of the charging energy to superconducting gap.