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.