It has previously been found that a magnetic impurity in a conventional$s$-wave superconductor can give rise to a local $\pi$-phase shift of thesuperconducting order parameter. By studying a finite wire of ferromagneticimpurities, we are able to trace the origin of the $\pi$-phase shift to aresonance condition for the Bogoliubov-de Gennes quasiparticle states. Whennon-resonating states localized at the impurity sites are pulled into thecondensate for increasing magnetic strength, the superconducting orderparameter is reduced in discrete steps, eventually resulting in a $\pi$-phaseshift. We also show that for a finite spin-orbit coupling, the $\pi$-phaseshift is preserved and occurs in a large portion of the topologicallynon-trivial phase.
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机译：先前已经发现，常规的波超导体中的磁性杂质会引起超导阶数参数的局部ππ相移。通过研究铁磁杂质的有限导线，我们能够追踪Bogoliubov-de Gennes准粒子状态的$ \ pi $相移到谐振条件的起源。当位于杂质位点的非共振态被拉入冷凝物中以增加磁强度时，超导阶跃参数将以离散步长减小，最终导致π/π相移。我们还表明，对于有限的自旋轨道耦合，$ \ pi $相移得以保留，并发生在拓扑非平凡相的很大一部分中。
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