Superconductor-insulator transition in two-dimensional NbN/MgO and NbN/AlN/MgO films

In this study, we investigate the dependence of superconducting transition temperature (T-c) on sheet resistance (R-sq) for two series of NbN films with different homogeneities which were prepared on either MgO substrates (NbN/MgO) or MgO substrate covered with a 1nm thick AlN layer (NbN/AlN/MgO). The R-sq-dependent T-c(T-c(R-sq)) behavior of the homogeneous NbN/MgO films could be explained with Finkel'stein's formula, which is based on localization theory using reasonable fitting parameters. On the other hand, the T-c(R-sq) values of the NbN/AlN/MgO films were larger than that of the NbN/MgO films in the region Rsq >= Rsq* approximate to 300 similar to 400 Omega. To understand the origin of this deviation from the theory for homogeneous systems, we assumed that the NbN/AlN/MgO films have the potential to form an inhomogeneous percolation structure. To confirm this assumption, the temperature (T) dependence of the upper critical magnetic field (H-c2(T)) near T-c was analyzed using the form H-c2(T) proportional to (1 - T/T-c)(2/(2+theta)) which is based on classical percolation theory. From the theta dependence of R-sq(theta(R-sq)) of both series, it was found that the theta(R-sq) of the NbN/AlN/MgO films deviates in the region R-sq >= R-sq** approximate to 150 similar to 200 Omega from theta = 0 in a homogeneous NbN/MgO films. By introducing an effective sheet resistance R-sq(eff.)(<R-sq) to account for the inhomogeneous structure of the NbN/AlN/MgO films, we were able to qualitatively explain the differences between the T-c(R-sq) behaviors of the two series.