标题： 磁性杂质在宽能带s波超导体中诱导的能隙态：自洽计算 显示英文标题

标题： In-gap states induced by magnetic impurities on wide-band s-wave superconductors: self-consistent calculations

摘要： 在s波超导体中由磁性杂质产生的能隙内态的研究中，自洽性在Bogoliubov-de Gennes方程中的作用经常被低估。 我们的研究集中在自洽性对磁性结构在超导体上产生的能隙内态的影响，特别是评估态密度、能隙带及其拓扑属性。 在这里，我们展示了从单个杂质到有限链以及宽能带s波超导体中的无限铁磁自旋链的结果。 这些结果表明，序参量包含有关量子相变及其拓扑性质的重要信息，强调了在这些研究中自洽性的重要性。 显示英文摘要

摘要： 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.