Fig. 4: Anderson impurity model for Yu-Shiba-Rusinov bound states.

a Local density of states as a function of level energy ϵ₀. The impurity spectral function was calculated within the zero-bandwidth approximation using the Lehmann spectral representation for the retarded Green’s function (see Supplementary Note 2). Red and blue lines indicate the two different ϵ₀ sweeps plotted in b and c, respectively. b, c Relaxation dominated tunneling conductance calculated to leading order in the tip-impurity tunneling rate Γ_t. Labels in b refer to processes in d. The dashed line in c shows the turning point of the blue line in a. d Guide to the eye for different conductance contributions in b and c. Processes 2–3 require a finite population of the excited state, in this case supplied by temperature. For all panels we use U = 20, Γ_s = 3, Γ_t = 0.04, γ = Γ_r = 0.035 and k_BT = 0.2, all in units of Δ_s.