Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions

@article{Heck2011CoulombSO,
  title={Coulomb stability of the 4$\pi$-periodic Josephson effect of Majorana fermions},
  author={Bernard van Heck and Fabian Hassler and A. Akhmerov and C. W. J. Beenakker},
  journal={Physical Review B},
  year={2011},
  volume={84},
  pages={180502}
}
The Josephson energy of two superconducting islands containing Majorana fermions is a 4\pi-periodic function of the superconducting phase difference. If the islands have a small capacitance, their ground state energy is governed by the competition of Josephson and charging energies. We calculate this ground state energy in a ring geometry, as a function of the flux -\Phi- enclosed by the ring, and show that the dependence on the Aharonov-Bohm phase 2e\Phi/\hbar remains 4\pi-periodic regardless… 

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One can distinguish the two currents by their size dependence: While I N decays as 1/R or faster, I J has the R independence of a supercurrent
    The flux induced by the supercurrent I J due to the nonzero inductance L μ 0 R of the ring may be neglected relative to the applied flux if LI J h/e. The magnitude of the supercurrent can be