Modeling the microwave properties of superconductors

In this paper a macroscopic phenomenological model for the microwave properties of superconductors is presented. The model is based on the idea that there are two kinds of current carriers, and instead of the first London´s equation a new equation is derived. This model can be applied to both low- and high-temperature superconductors. Using this model, an expression for the microwave surface resistance is derived and the surface resistance versus frequency is calculated. The results show that the relation between resistance and frequency is not R₃~ω² as indicated by both BCS theory and London model, but R_s~ω^a, where a is between 1 and 2 (e.g. a=1.35) for thin film high-T_c superconductors YBa₂Cu₃O_7-δ. The temperature dependence of R_s is simulated using the given model. These relations and the values of the surface resistance agree well with experimental results. A residual resistance may be interpreted from this model