TY - JOUR

T1 - Josephson current in a normal-metal nanowire coupled to a superconductor/ferromagnet/superconductor junction

AU - Ebisu, H.

AU - Lu, B.

AU - Taguchi, K.

AU - Golubov, Alexandre Avraamovitch

AU - Tanaka, Y.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - METIS-320372

KW - IR-103514

U2 - 10.1103/PhysRevB.93.024509

DO - 10.1103/PhysRevB.93.024509

M3 - Article

VL - 93

SP - 024509-

JO - Physical review B: Condensed matter and materials physics

JF - Physical review B: Condensed matter and materials physics

SN - 1098-0121

IS - 024509

M1 - 024509

ER -