It has previously been found that a magnetic impurity in a conventional s-wave superconductor can give rise to a local π-phase shift of the superconducting order parameter. By studying a finite wire of ferromagnetic impurities, we are able to trace the origin of the π-phase shift to a resonance condition for the Bogoliubov-de Gennes quasiparticle states. When nonresonating states localized at the impurity sites are pulled into the condensate for increasing magnetic strength, the superconducting order parameter is reduced in discrete steps, eventually resulting in a π-phase shift. We also show that for a finite spin-orbit coupling, the π-phase shift is preserved and occurs in a large portion of the topologically nontrivial phase.
Physical Review B