Fractional Josephson Effect in Number-Conserving Systems

Abstract

We study fractional Josephson effect in a particle-number conserving system consisting of a quasi-one-dimensional superconductor coupled to a nanowire or an edge carrying $e/m$ fractional charge excitations with $m$ being an odd integer. We show that, due to the topological ground-state degeneracy in the system, the periodicity of the supercurrent on magnetic flux through the superconducting loop is non-trivial which provides a possibility to detect topological phases of matter by the $dc$ supercurrent measurement. Using a microscopic model for the nanowire and quasi-one-dimensional superconductor, we derived an effective low-energy theory for the system which takes into account effects of quantum phase fluctuations. We discuss the stability of the fractional Josephson effect with respect to the quantum phase slips in a mesoscopic superconducting ring with a finite charging energy.

16 pages, 7 figures; revised version, new section added

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• Fermionized parafermions and symmetry-enriched Majorana modes
• Majorana zero modes choose Euler numbers - revealed by full counting statistics
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• Josephson junction detectors for Majorana modes and Dirac fermions
• Parafermionic generalization of the topological Kondo effect
• Magnetization induced dynamics of a Josephson junction coupled to a nanomagnet
• Parafermions in a multilegged geometry: Towards a scalable parafermionic network
• Majorana zero modes and their bosonization
• Proposal for measuring the parity anomaly in a topological superconductor ring
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