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

摘要

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 similar to exp[-vertical bar n vertical bar/xi], where n is the site index and the xi 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 xi. We find that when xi 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 sin 2 phi, where phi 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 sin 2 phi dependence in the current-phase relation. We further study both the energy and phi dependence of pair amplitudes in the ferromagnetic region. For large xi, 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.