Nonlinear Surface Reactance of a Superconductor Strip

The nonlinear reactive response of a thin superconductor strip at microwave frequencies is analyzed in terms of two mechanisms intrinsic to a superconductor: the response of the condensate state in the presence of an electromagnetic transversal field and the Lorentz-force effect. These are qualitatively and quantitatively distinct mechanisms. The former is a quantum effect, at work at the strip midsection where the current density is approximately constant, while the latter is a classical effect associated with the large current gradients at the strip edges. The lowest nonlinear term in the penetration depth is calculated for both mechanisms in the static limit and for an s-wave superconductor. The result associated with the condensate state response mechanism compares well with recent high-quality YBCO-film data, particularly at elevated temperatures. On the other hand the Lorentz force nonlinearity mechanism yields a negligible contribution for a wide thin film. We conclude with a brief discussion of this work in perspective to related work.