Intermodulation distortion and surface resistance in impurity-doped YBCO and MgB2

•Calculations of impurity-doping effects on surface resistance and intermodulation distortion.•The calculations are compared with previously published measurements in YBCO and MgB2.•Excellent agreement between calculations and experiments are shown.•The effects of the symmetry of the energy gap are presented and discussed.

Calculations of the microwave intermodulation distortion (IMD) and surface resistance of impurity-doped YBCO, MgB2 and Nb are presented. These are qualitatively distinct superconductors due to their energy-gap symmetries, d-wave (ℓ = 2), i-wave (ℓ = 6) and s-wave (ℓ = 0), respectively. The calculations are compared with previously published IMD and surface-resistance measurements of impurity-doped YBCO and Nb. The agreement between the data and fitted calculations is excellent in all cases. In the absence of IMD and surface-resistance measurements for doped MgB2, we present representative predictions. The calculations are based on a Green’s-function approach that yields analytical expressions for the penetration depth and the nonlinear kernel in the constitutive relation. This penetration-depth expression reproduces the measured T2 low-temperature variation for doped superconductors and the surface-resistance reduction over that of the pure material. Regarding the IMD in superconductors with a nodal energy gap, the effect of doping is to enhance its magnitude and suppress its low-temperature 1/T2 divergence predicted by the nonlinear Meissner effect.