Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

H. Ebisu, B. Lu, K. Taguchi, Alexandre Avraamovitch Golubov, Y. Tanaka

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We consider a superconducting nanowire proximity coupled to a superconductor/ferromagnet/superconductor (S/F/S) junction, where the magnetization penetrates into a superconducting segment in a nanowire decaying as ∼exp[−∣n∣ξ], where n is the site index and the ξ is the decay length. We tune chemical potential and spin-orbit coupling so that the topological superconducting regime hosting the Majorana fermion is realized for long ξ. We find that when ξ becomes shorter, zero energy state at the interface between a superconductor and a ferromagnet splits into two states at nonzero energy. Accordingly, the behavior of the Josephson current is drastically changed due to this “zero mode-nonzero mode crossover.” By tuning the model parameters, we find an almost second-harmonic current-phase relation sin2φ, where φ is the phase difference of the junction. Based on the analysis of Andreev bound state (ABS), we clarify that the current-phase relation is determined by coupling of the states within the energy gap. We find that the emergence of crossing points of ABS is a key ingredient to generate sin2φ dependence in the current-phase relation. We further study both the energy and φ dependence of pair amplitudes in the ferromagnetic region. For large ξ, an odd-frequency spin-triplet s-wave component is dominant. The magnitude of the odd-frequency pair amplitude is enhanced at the energy level of ABS.
Original languageEnglish
Article number024509
Pages (from-to)024509-
JournalPhysical review B: Condensed matter and materials physics
Issue number024509
Publication statusPublished - 2016


  • METIS-320372
  • IR-103514


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