Fig. 1. Schematic illustration (a) and equivalent circuit (b) of the two-coil mutual inductance apparatus.

Fig. 2. (a) The mutual inductance as a function of film radii R calculated for the typical superconducting film with d = 100 nm, λ = 150 nm; (b) calculations of penetration depth λ_cal vs film radii R for different spacings between two coils (h = 0.9, 4.5, 9.0 mm). The real penetration depth (λ = 150 nm) is indicated by the dotted line.

Fig. 3. (a) The induced voltage data V_{x, 1}(T) and V_{x, 2}(T) taken from the same Nb film with sample remounted; (b) the frequency dependence of induced voltage V(T = 4.5 K) for the Nb film.

Fig. 4. Two-coil mutual inductance measurement results of NbN films (NbN#1, NbN#2, NbN#3, NbN#4): (a) Temperature dependence of induced voltage V_x(T) and V_y(T) for NbN#1; (b) temperature-dependent penetration depth λ(T) of four NbN films; (c) temperature variation in superfluid density for NbN#1. The black line shows the dirty s-wave BCS theory fit to the data; (d) the value of λ(T→ 0) for four NbN films, which shows a good agreement with the published value^[38]. The length of error bar is shorter than the symbol size.