Broadened Yu-Shiba-Rusinov states in dirty superconducting films and heterostructures

Abstract

The interplay of a potential and magnetic disorder in superconductors has remained an active field of research for decades. Within the framework of the Usadel equation, we study the local density of states (LDOS) near a solitary classical magnetic impurity in a dirty superconducting film. We find that a potential disorder results in broadening of the $\ensuremath{\delta}$-function peak in the LDOS at the Yu-Shiba-Rusinov (YSR) energy. This broadening is proportional to the square root of a normal-state spreading resistance of the film. We demonstrate that modification of multiple scattering on the magnetic impurity due to intermediate scattering on surrounding potential disorder crucially affects a profile of the LDOS in the vicinity of the YSR energy. In addition, we find that a scanning-tunneling-microscopy tip can mask a YSR feature in the LDOS. Also, we study the LDOS near a chain of magnetic impurities situated in the normal region of a dirty superconductor/normal-metal junction. We find a resonance in the LDOS near the YSR energy. The energy scale of the resonant peak is controlled by the square root of the film resistance per square in the normal state.