We study the Josephson effect in a clean noncentrosymmetric superconductor/half-metal/noncentrosymmetric superconductor junction, which is grown on the surface of a three-dimensional Topological Insulator (TI) in the ballistic limit. We find the signature of anomalous Andreev Bound States (ABS) and band splitting for a spin-active barrier whose barrier magnetic moment is misaligned with the bulk moment. The chiral Majorana mode and 4$\pi$ periodic ABS are found to exist on the surface of TI for parallel orientation of the moments in the normal incidence condition. But for anti-parallel misalignment, we observe the 2$\pi$ periodic ABS. There exist a gap in ABS for oblique incidence. We find the splitting of Andreev levels in the presence of RSOC and also for unequal mixing of singlet–triplet correlations present in NCSC. The Majorana mode, ABS and Josephson supercurrent can be controlled by the ratio of barrier magnetic and non-magnetic moments. The critical current is found to be maximum for singlet or triplet dominated NCSC, while it is minimum in the equal mixing condition. The ABS is found to be barrier thickness dependent and is suppressed for an opaque barrier. We observe a monotonic decay in critical current with a finite length of the junction for all the singlet–triplet mixings and magnetic moments. The current-phase relation is found to be sinusoidal with no phase shift in the half-metallic limit, however, for different orientations of the bulk moment, an anomalous characteristic is also observed.

我们研究了干净的非中心对称超导体/半金属/非中心对称超导体结中的约瑟夫森效应，该结在弹道极限的三维拓扑绝缘体 (TI) 的表面上生长。我们发现了自旋活性势垒的异常安德列夫束缚态 (ABS) 和能带分裂的特征，其势垒磁矩与体矩未对齐。手性 Majorana 模式和 4$\pi$发现周期性 ABS 存在于 TI 表面，用于在法向入射条件下平行取向的矩。但是对于反平行错位，我们观察到 2$\pi$定期 ABS。ABS 在斜入射方面存在差距。我们发现在存在 RSOC 的情况下 Andreev 水平的分裂以及 NCSC 中存在的单线态-三线态相关性的不均匀混合。Majorana 模式、ABS 和约瑟夫森超电流可以通过势垒磁矩和非磁矩的比率来控制。发现临界电流对于单线态或三线态为主的 NCSC 最大，而在等混合条件下最小。发现 ABS 与阻挡层厚度有关，并且在不透明阻挡层中被抑制。对于所有单线态-三线态混合和磁矩，我们观察到临界电流的单调衰减，结的长度有限。电流-相位关系被发现是在半金属极限内没有相移的正弦曲线，然而，对于不同方向的体积矩，