Calculation of penetration depth under various numerical models for the reflection-type two-coil mutual inductance technique

The two-coil mutual inductance (TCMI) technique is a useful experimental method to derive the magnetic penetration depth λ in a superconducting film after proper numerical calculations, in which various film geometries including infinite, circular and quadrangle films have been utilized. Based on previously reported reflection-type TCMI experimental data taken from NbN and K-adsorbed FeSe thin films, we investigate the validity of various numerical models with different geometries by comparing their calculation results. The calculated values of λ for various film geometries become identical only when the film size is at least three times larger than the coil size. For a rectangular film with a width comparable to the coil size, the numerical models of circular and square film geometries with proper sizes can also be adopted to obtain a similar λ value as that calculated with a rectangular film geometry. Although the true value of λ can be approximately achieved only after a complicated calibration, its calculated temperature dependence is insensitive to the choice of numerical models. With these results, a proper film geometry for the numerical calculation of λ may be selected to effectively improve the calculation efficiency.