Review of Yu–Shiba–Rusinov bound state in quantum impurity structures: basic principle and current progress

Abstract Magnetic impurities connected to superconductors reservoir result in bound states within the superconducting gap, so called Yu–Shiba–Rusinov (YSR) state. In the past few years, this field has gained much attention since it is crucial for engineering novel superconducting many-body states, with the perspective of manufacturing Majorana Fermions. The underlying physical picture of YSR state depends closely on the form of the impurities connected to the leads, the manner in which the impurities are organized, and also the diverse local interactions, which is always disclosed with the aid of quantum impurity models. This article provides a comprehensive overview of the progress achieved by previous studies, focusing on the issues demonstrated by quantum impurity structures. The physical mechanisms and the related phenomena assisted by different interactions are discussed in detail. Furthermore, a comprehensive overview of recent experimental achievements is presented, using various metal phthalocyanine molecules as illustrative examples, thereby establishing a robust foundation for future inquiries in this domain.