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.
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机译:我们考虑耦合到超导体/铁磁体/超导体(S / F / S)结的超导纳米线邻近,其中磁化强度渗透到纳米线中的超导段中,衰减为〜exp [-∣n∣ξ],其中n是位置指数,ξ为衰减长度。我们调整化学势和自旋轨道耦合,以便实现容纳马里亚纳费米子的拓扑超导体系长ξ。我们发现,当ξ变短时,超导体和铁磁体之间的界面处的零能量状态在非零能量处分裂为两个状态。因此,由于这种“零模式-非零模式交叉”,约瑟夫森电流的行为发生了巨大变化。通过调整模型参数,我们发现几乎是二次谐波的电流-相位关系sin2φ,其中φ是结的相位差。基于对Andreev束缚态(ABS)的分析,我们阐明了电流-相位关系是由能隙内的状态耦合确定的。我们发现,ABS交叉点的出现是在电流-相位关系中产生sin2φ依赖性的关键因素。我们将进一步研究铁磁区域中对振幅的能量和φ依赖性。对于较大的ξ,奇数频率自旋三重态s波分量占主导地位。在ABS的能级上,奇数频率对幅度的幅度增加了。
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