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arXiv · 1108.1095

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

B. van Heck·F. Hassler·A. R. Akhmerov·C. W. J. Beenakker
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Abstract

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 of the ratio of charging and Josephson energies - provided that the entire ring is in a topologically nontrivial state. If part of the ring is topologically trivial, then the charging energy induces quantum phase slips that restore the usual 2\pi-periodicity.

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B. van Heck, F. Hassler, A. R. Akhmerov, C. W. J. Beenakker. 2011-08-04. Coulomb stability of the 4\pi-periodic Josephson effect of Majorana fermions. https://doi.org/10.1103/physrevb.84.180502

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