We theoretically investigate how the spin susceptibility of a planar Josephson junction is affected when the system transits into the topological superconducting state. We show that the magnetic flux and magnetic field dependence of the spin susceptibility closely maps the phase diagram of the system. In the absence of an external magnetic flux the system can self-tune into the topological superconducting state by minimizing its free energy. Self-tuned topological transitions are accompanied by sharp peaks in the spin susceptibility, which can therefore be used as measurable fingerprints for detecting the topological superconducting state. Away from the peaks, the amplitude of the spin susceptibility can provide qualitative information about the relative size of the topological gap. The signatures in the spin susceptibility are robust, even in junctions with narrow superconducting leads, where critical current minima may no longer serve as an indication of topological phase transitions. The predicted results could be particularly relevant for future experiments on realization and detection of the topological superconducting state in planar Josephson junctions.

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约瑟夫森结自旋磁化率的拓扑跃迁特征

我们从理论上研究了当系统转变为拓扑超导状态时平面约瑟夫森结的自旋敏感性如何受到影响。我们表明自旋磁化率的磁通量和磁场依赖性紧密地映射了系统的相图。在没有外部磁通量的情况下，系统可以通过最小化其自由能来自调谐到拓扑超导状态。自调谐拓扑跃迁伴随着自旋磁化率的尖峰，因此可以用作检测拓扑超导状态的可测量指纹。远离峰值，自旋磁化率的幅度可以提供关于拓扑间隙相对大小的定性信息。自旋敏感性的特征是稳健的，即使在具有窄超导引线的结中，临界电流最小值可能不再作为拓扑相变的指示。预测结果可能与未来实现和检测平面约瑟夫森结中拓扑超导状态的实验特别相关。