Temperature dependence of intermodulation distortion in YBCO: understanding nonlinearity

Intermodulation distortion (IMD) in high-T_c superconductor (HTS) devices continues to be important, and a complete understanding is lacking. We have measured the third-order IMD vs power as a function of temperature from 1.7 K to T_c for YBCO films of several fabrication methods on lanthanum aluminate and sapphire. The measurements used a stripline resonator at either 1.5 GHz or 2.3 GHz depending on the substrate. The results show increasing IMD with decreasing temperature at low power levels. The IMD diverges nearly as 1/T² for temperatures below 5 K. This temperature and power dependence of the IMD is an observation of the nonlinear Meissner effect that has been predicted for superconductors with d-wave symmetry but has not been previously observed. The results agree with a rigorous, many-body calculation that yields directly the lowest-order correction of the nonlinear penetration depth as a function of the current. We discuss the role of intrinsic and extrinsic properties in the IMD. We also discuss the implications for practical devices operated at usual cryocooler temperatures.