Determining the absolute value of magnetic penetration depth in small-sized superconducting films

In the previous four decades, the two-coil mutual inductance (MI) technique has been widely employed in characterizing magnetic penetration depth, lambda, of superconducting films. However, the conventional methods used to obtain lambda are not applicable to small-sized films with common shapes, which limits the application of the MI technique in superconductivity research. Here, we first employed the fast wavelet collocation (FWC) method to a two-coil system and then proposed the possibility of directly obtaining the absolute lambda of polygonal superconducting films with arbitrary sizes. To verify its accuracy and advantages, we extracted the lambda values of square NbN films with different sizes using the FWC and conventional flux leakage subtraction (FLS) methods. Notably, the FLS method fails for a 5x5 mm(2) film, which is attributed to the significant current peak at the film edge. In contrast, the absolute lambda extracted using the FWC method was independent of the film size. Finally, we established the applicability of the FWC method to large coil spacings, which may pave the way for integrating high-accuracy lambda measurements with the ionic liquid gating technique.