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.
تحميل البحث