A quantitative theory of Yu-Shiba-Rusinov states of magnetic atomic structures on different superconducting substrates

Based on a fully relativistic multiple scattering approach combined with the solution of Bogoliubov--de Gennes equations it is possible to study the spectral properties of different magnetic impurities on various superconducting substrates in a material-specific framework. These systems have attracted considerable interest since they serve as building blocks of Kitaev chains playing an important role in the quest of finding Majorana states. The understanding of the characteristic features provided by even a single impurity is essential for the design of nanosystems that can host Majorana zero modes.

We performed calculations for different s-wave superconductors (Nb, Ta, Pb), covered by different overlayers (Au, Ir, Pt, Bi) hosting different magnetic impurities (Mn, Fe, Co, Cr). The local density of states (LDOS) is calculated for each system within the superconducting gap, and the formation of the Yu--Shiba--Rusinov states is observed. The YSR spectrum is analyzed with respect to the LDOS in the normal state and the effect of spin-orbit coupling is studied. In several systems, we found signatures of spin-triplet superconductivity via the coupling between the electron and hole spin-down channels induced by large spin-orbit interaction, which we further verified in terms of the calculated spin-triplet order parameter.