  The role of self-consistency in Bogoliubov-de Gennes equations is frequently
underestimated in the investigation of in-gap states created by magnetic
impurities in s-wave superconductors. Our research focuses on the impact of
self-consistency on the in-gap states produced by magnetic stuctures on
superconductors, specifically evaluating the density of states, the in-gap
bands, and their topological attributes. Here, we show results ranging from
single impurity to finite chains, and infinite ferromagnetic spin chains in
wide-band s-wave superconductors. These results show that the order parameter
contains important information regarding quantum phase transitions and their
topological nature, underscoring the importance of self-consistency in such
studies.
