Mesoscopic magnetism and superconductivity

Superconductivity and magnetism at intermediate (“mesoscopic”) length scales between atomic and bulk have a long history of interesting science. New science emerges due to the presence of multiple length scales, especially when these become comparable to relevant geometric sizes. New phenomena may appear due to topological interactions, geometric confinement, proximity between dissimilar materials, dimensional crossover, and collective effects induced by periodicity. In this review, we select a few, recent highlights that illustrate the type of novel science that can be accomplished in superconducting and magnetic structures. These materials can serve as model systems and provide new ideas, which can be extended to other systems such as ferroelectrics and multiferroics. We also highlight general open questions and new directions in which the field may move.