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

机译:马里亚纳费米子的4π周期约瑟夫森效应的库仑稳定性

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摘要

The Josephson energy of two superconducting islands containing Majorana fermions is a 4π-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 φ enclosed by the ring, and show that the dependence on the Aharonov-Bohm phase 2eΦ/h remains 4π 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 2π periodicity.
机译:两个包含马里亚纳费米子的超导岛的约瑟夫森能量是超导相差的4π周期函数。如果这些岛的电容较小,则其基态能量将由约瑟夫森和充电能量的竞争所支配。我们根据环形物所包围的通量φ来计算环形物中的基态能量,并表明,无论充电和约瑟夫森能量的比值如何,对Aharonov-Bohm相2eΦ/ h的依赖性都保持4π周期-假设整个环处于拓扑非平凡状态。如果环的一部分在拓扑上是微不足道的,则充电能量会引起量子相位滑移,从而恢复通常的2π周期性。

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