Description of the nonlinear behavior of superconductors using a complex conductivity

The origin of the detrimental nonlinear response in high T_c superconductor (HTS) microwave devices is currently not well understood. In order to help elucidate the origin of these nonlinear effects, we have developed a description of the nonlinear response in superconductors in terms of a current-dependent complex conductivity. We demonstrate that such a treatment can consistently describe the results of power-dependent surface impedance measurements in resonator geometries as well as harmonic generation and intermodulation distortion effects in transmission line geometries. This approach yields a device-independent quantity that describes the nonlinear response of the superconducting material itself, which is suitable for comparisons of different materials and for material optimization. A further benefit of this description of nonlinear effects is that the relative importance of the nonlinear resistive and inductive components of a superconductor can be examined. We use this approach to predict the phase of the nonlinear response in HTS planar transmission lines, and compare our predictions with new phase-sensitive measurements made using a nonlinear vector network analyzer.