Nonlinear inductive response of pinned superconducting vortices in artificial pinning sites

Using the time dependent Ginzburg - Landau (TDGL) equations, we simulate the inductive responses of a variety of thin film systems containing patterned anti-dots with differing sizes and shapes. The results for all shapes show that the kinetic inductance diverges as the applied current approaches a critical current, J_c, which is below the BCS depairing current, J_dp. Exploiting the similarity of the observed E-J behavior to that modeled by a critical exponent near a second phase transition, we obtain an empirical equation that well fits the effective inductivity curve as a function of the applied current.