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

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

2011-08-04

arxiv.org/abs/1108.1095v2

Phys. Rev. B 84, 180502(R) (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures; v2: more references, improved phase-slip formula, and a discussion of the effect of overlapping Majorana's

Scientific paper

10.1103/PhysRevB.84.180502

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 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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