The interplay of a potential and magnetic disorder in superconductors remains an active field of research for decades.Within the framework of the Usadel equation [1], we study the local density of states near a solitary classical magnetic impurity in a dirty superconducting film [2]. We find that a potential disorder results in broadening of the delta-function peak in the local density of states at the Yu-Shiba-Rusinov (YSR) energy [3-5]. 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 affects crucially a profile of the local density of states in the vicinity of the YSR energy.
[1] K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
[2] S. S. Babkin et al., arXiv:2201.11723 (2022).
[3] L. Yu, Acta Phys. Sin. 21, 75 (1965).
[4] H. Shiba, Prog.Theor. Phys. 40, 435 (1968).
[5] A. I. Rusinov, Zh. Eksp.Teor. Fiz. 56, 2047 (1969).