A current-density scale for characterizing nonlinearity in high-Tc superconductors

In this paper, we characterize microwave nonlinearity in a high temperature superconducting (HTS) thin-film by measuring a geometry-independent current-density scale j_o. The quantity j_o specifies the strength of a material-dependent nonlinearity, and can be used to calculate the nonlinear microwave response of planar superconducting transmission-line devices. Our procedure for determining j_o involves microwave measurements on superconducting coplanar waveguide devices patterned onto the HTS sample. In a YBa₂Cu₃O_7-x (YBCO) sample, we obtained a maximum experimental value for j_o of approximately 3.26×10⁸ A/cm² at 25 K. From the measured temperature-dependence of j_o in our YBCO sample, and assuming a theoretical pair-breaking current density j_c equal to 3×10⁸ A/cm², we calculated the temperature dependence of the quasiparticle factor b(T). The curve of the experimentally obtained b(T) matched well with a theoretically-predicted behavior in the scenario of d-wave symmetry in the superconducting order parameter.