AI 中文总结
该研究从理论上探讨含双极磁性半导体（BMS）的约瑟夫森结，实现了无需外磁场的0-π跃迁电控制，发现了反常约瑟夫森效应但未观测到约瑟夫森二极管效应，明确了反常输运与超导非互易性的区别。
AI 中文摘要
我们从理论上研究了包含双极磁性半导体（BMS）的一维约瑟夫森结中的平衡电流。结果表明，自旋分辨能带的本征交换劈裂可通过门控调谐BMS的化学势实现0-π跃迁的纯电学控制，无需外部磁场，为电可调π结行为提供了可行途径，并凸显了基于BMS的约瑟夫森器件在相位可控超导电子学中的潜力。此外，在存在Rashba自旋-轨道耦合时，我们发现了反常约瑟夫森效应，其特征为零相位差下存在有限平衡超电流，该行为源于BMS自旋极化电子结构相关的时间反演对称性自发破缺。值得注意的是，尽管时间反演与空间反演对称性同时破缺（这类条件通常与非互易超导输运相关），我们并未观测到约瑟夫森二极管效应。因此，我们的结果凸显了反常约瑟夫森输运与超导非互易性之间的重要区别：前者并不一定意味着相反电流方向间存在有限的临界电流不对称性。
英文摘要
We theoretically investigate equilibrium currents in a one-dimensional Josephson junction incorporating a bipolar magnetic semiconductor (BMS). We show that the intrinsic exchange splitting of the spin-resolved bands enables purely electrical control of the $0$--$π$ transition through gate-tunable modulation of the BMS chemical potential, eliminating the need for an external magnetic field. This provides a viable route toward electrically tunable $π$-junction behavior and highlights the potential of BMS-based Josephson devices for phase-controllable superconducting electronics. Furthermore, in the presence of Rashba spin--orbit coupling, we find an anomalous Josephson effect characterized by a finite equilibrium supercurrent at zero phase difference. This behavior originates from the intrinsic breaking of time-reversal symmetry associated with the spin-polarized electronic structure of the BMS. Interestingly, despite the simultaneous breaking of time-reversal and inversion symmetries---conditions often associated with nonreciprocal superconducting transport---we do not observe a Josephson diode effect. Our results therefore highlight an important distinction between anomalous Josephson transport and superconducting nonreciprocity: the former does not necessarily imply a finite critical-current asymmetry between opposite current directions.
Comments6 pages, 5 captioned figures. Comments are welcome
