Shiba states in systems with density of states singularities

Magnetic impurities placed in the superconductor can lead to emergence of Yu-Shiba-Rusinov bound states. Coupling between impurity and substrate depends on density states (DOS) at Fermi level be tuned by DOS singularities. In this paper, we study role singularities using real space Bogoliubov-de Gennes equations for chosen lattice models. To uncover these (Dirac point, van Hove singularity, or flat band), honeycomb, kagome, Lieb lattices. We show that properties Shiba state strongly type lattice. Nevertheless some behaviors are generic, e.g. dependence critical magnetic coupling level. However, realized exhibit extraordinary properties, which explained presence a few nonequivalent sublattices. Depending location sublattice, value $J_\text{c}$ reduced enhanced when band is located context, also present differences local coherence lengths different sublattices