Vortex pairs and nonlinear inductance of high-Tc superconducting microwave resonators

Recently, an unusual power dependence of two-tone intermodulation has been observed in high-T_c superconducting microwave resonators. In order to address this problem, we study the nonlinear response of a two dimensional Josephson junction array as a coupled grain model for the high-T_c films. On a microscopic scale the calculated current distributions within the array show a strong tendency to form topological Josephson vortices which organize themselves in vortex-antivortex clusters even in the absence of an external magnetic field. These vortex clusters are stable within an external ac drive and cause a redistribution of the input current. The resulting current distributions possess pronounced transversal components. On the macroscopic scale such current distributions lead to a nonlinear inductance that varies linearly with the magnitude of the input current consistent with the observed power dependence. This result suggests the dynamics of topological Josephson vortices within the coupled grains as a possible explanation for the unusual nonlinear response