Coulomb Blockade of a Nearly Open Majorana Island

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 R. The amplitude scales as root R in the limit R -> 0. At larger 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 R is small and depends on the ratio of the charging energy to superconducting gap.