Nonlinear inductive response of pinned superconducting vortices in artificial pinning sites

Using the time dependent Ginzburg-Landau equations, we simulate the inductive responses of a variety of thin-film systems containing patterned antidots with different sizes and shapes. The results for all shapes show that the kinetic inductance diverges as the applied current approaches a critical current that is below the BCS depairing current. Exploiting the similarity of the observed current-voltage behavior to that of Josephson junctions, we obtain an empirical equation that well fits the inductivity curve as a function of the applied current.