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 non-resonating 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 non-trivial phase.
@article{arxiv.1609.07626,
title = {Superconducting order parameter $\pi$-phase shift in magnetic impurity wires},
author = {Kristofer Björnson and Alexander. V. Balatsky and Annica M. Black-Schaffer},
journal= {arXiv preprint arXiv:1609.07626},
year = {2017}
}