Abstract

Motivated by recent STM experiments, we study lattices of magnetic adatoms exchange coupled to the surface of a conventional s-wave superconductor. In this talk, I demonstrate how a variety of collective magnetic and electronic phases emerge in this system, due to the interplay between ferromagnetism and superconductivity. In particular, an adatom chain on a bulk (2D or 3D) superconductor can order into a magnetic spiral state leading to, and stabilized by, the opening of a topological superconducting gap within the band of Yu-Shiba-Rusinov (YSR) sub-gap states induced by the magnetic moments. In two dimensions, a square lattice of magnetic moments is shown to exhibit strong magnetic frustration due to the long-ranged indirect exchange coupling mediated by the hybridization of YSR states. Finally, I shall touch upon recent experiments on transport through artificial magnetic adatoms realized in single, and double quantum dots, – a perfect lab for studying the physics of individual YSR states.