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The Josephson energy of two superconducting islands containing Majoranafermions is a 4\pi-periodic function of the superconducting phase difference.If the islands have a small capacitance, their ground state energy is governedby the competition of Josephson and charging energies. We calculate this groundstate energy in a ring geometry, as a function of the flux -\Phi- enclosed bythe ring, and show that the dependence on the Aharonov-Bohm phase 2e\Phi/\hbarremains 4\pi-periodic regardless of the ratio of charging and Josephsonenergies - provided that the entire ring is in a topologically nontrivialstate. If part of the ring is topologically trivial, then the charging energyinduces quantum phase slips that restore the usual 2\pi-periodicity.

Coulomb stability of the 4\pi-periodic Josephson effect of Majorana fermions