Classification of Yu-Shiba-Rusinov states of magnetic impurities on superconducting surfaces: A fully relativistic first-principles study

Magnetic adatoms at surfaces of superconductors may induce localized bound states within the superconducting energy gap referred to as Yu-Shiba-Rusinov (YSR) states. We solve the Kohn-Sham-Dirac Bogoliubov-de Gennes equations within the fully relativistic multiple scattering Green's function method to study the nature of the YSR states for 3d magnetic impurities (Cr, Mn, Fe, and Co) placed on a pristine Nb(110) surface, as well as capped by a monolayer of Bi, Re, or Ir. First, we perform self-consistent relativistic calculations in the normal state and determine the direction of the easy axis and the magnetic anisotropy energy. Then we study the relation between the electronic structure in the normal state and the YSR states. We show that the YSR states can be categorized according to the energy-resolved singlet and triplet order parameters as normal, superconducting singlet, or induced triplet states. Finally, we demonstrate that the rotation of the adatom magnetic moment shifts the energy of the YSR states as a consequence of the spin orbit coupling. During this rotation, some branches of the YSR states might cross the Fermi energy, implying that at certain paths in the configuration space a peak can be found at zero energy.