We have implemented the Bogoliubov-de Gennes equation in a screened Korringa-Kohn-Rostoker method for solving, self-consistently, the superconducting state for three-dimensional (3D) crystals including substitutional impurities. In this paper we extend this theoretical framework to allow for collinear magnetism and apply it to fcc Pb with 3D magnetic impurities. In the presence of magnetic impurities, there is a pair-breaking effect that results in in-gap Yu-Shiba-Rusinov (YSR) states which we decompose into contributions from the individual orbital character. We determine the spatial extent of these impurity states, showing how the different orbital character affects the details of the YSR states within the superconducting gap. Our work highlights the importance of a first-principles-based description which captures the quantitative details, making direct comparisons with experimental findings possible.
The above work was supported by the Centre for Doctoral Training in Condensed Matter Physics, funded by EPSRC Grant No. EP/L015544/1. T.G.S. gratefully acknowledges support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Grant No. TRR 173/2 - 268565370 Spin+X (project A11). G.C. gratefully acknowledges support from the European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 754510. This work was supported by Spanish MINECO (the Severo Ochoa Centers of Excellence Program under Grant No. SEV- 2017-0706), Spanish MICIU, AEI and EU FEDER (Grant No. PGC2018-096955-B-C43), and Generalitat de Catalunya (Grant No. 2017SGR1506 and the CERCA program). The work was also supported by the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143). M.G. thanks the visiting professorship program of the Centre for Dynamics and Topology at Johannes Gutenberg University Mainz.