Fig. 1: Uncorrelated disorder.

a Temperature dependence of the sample-averaged gap function \({\bar{\Delta }}_{\nu }\) for the strong band ν = 1 (red) and the weak band ν = 2 (blue), showing results for the cases when strong band is disordered (filled circles) and in its clean limit (empty circles). Low temperature \({T}_{c,2}^{(0)}\) is the critical temperature of the second band in the absence of inter-band coupling. Color density plot with the spatial distribution of the gap function Δ_1i (b) and Δ_2i (c) at temperature \(T=0.9\,{T}_{c}^{(0)}\). d Profile of the gap function for strong band ν = 1 (red) and weak band ν = 2 (blue), calculated along the dashed lines shown in b and c with \({\Delta }_{1}^{max}=0.365\) and \({\Delta }_{2}^{max}=0.085\). The minimum values of the gap function in the strong and weak bands are indicated by the red and blue dashed lines, respectively. e Histograms of the absolute value of the gap function for the strong band ν = 1 (red) and the weak band ν = 2 (blue). f Homogeneous contribution \({\Delta }_{2}^{(0)}\) to the gap in weak band ν = 2, compared between numerical calculations (circles) and estimates using Eq. (7). g Superfluid stiffness \({D}_{s,2}^{(0)}\) for weak band ν = 2 calculated for the cases when strong band ν = 1 is disordered (filled circles) and in the clean limit (empty circles). The dashed lines represent estimations \({D}_{s,2}^{(0)}\propto | {\Delta }_{2}^{(0)}{| }^{2}\) (orange) and \({D}_{s,2}^{(0)}\propto | {\bar{\Delta }}_{2}{| }^{2}\) (red).