Josephson current between two one-dimensional nanowires with proximity induced p-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-reflection is realized by means of two different channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters’ phase differences φ and oscillates with 4π period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from these channels and discuss experiments which can test our theory.

在存在拉什巴自旋轨道相互作用，面内磁场和法向磁场的情况下，计算了具有邻近感应p波超导对的两维一维纳米线之间的约瑟夫森电流。我们表明，Andreev后向反射是通过两个不同的通道实现的。约瑟夫森电流的主要贡献是在常规的粒子-空穴通道中产生散射，这是因为电子状的准粒子以相反的自旋反射到空穴状的准粒子时产生的电流仅取决于阶跃参数的相位差φ并振荡。与4π期。第二个异常粒子-空穴通道，对应于入射电子状准粒子对具有相同自旋取向的空穴状准粒子的安德列夫反射，仅在存在面内磁场时才存在。该通道对约瑟夫森电流的贡献不仅以φ以4π周期振荡，而且以面内磁场θ的取向角振荡，从而导致磁-约瑟夫森效应。在存在Rashba自旋轨道耦合（SOC）和法向平面磁场h的情况下，根据Andreev束缚态能量对相位φ和θ的依赖性，出现了一个禁隙在SOC强度和磁场的几个值下，约瑟夫森电流似乎消失了。我们对这种系统中的直流和交流约瑟夫森效应进行了详细的理论分析，显示了来自这些渠道的贡献，并讨论了可以验证我们理论的实验。