A calculation method by the improved three-fluid model is shown to describe phenomenologically temperature and frequency dependence of surface resistance Rs for high-Tc superconductors. It is verified that this model is useful to describe temperature dependence of Rs for such high-Tc superconducting films as Y-Ba-Cu-O (YBCO), Eu-Ba-Cu-O, and Tl-Ba-Ca-Cu-O films. For the frequency dependence of Rs of a YBCO bulk, furthermore, the measured results which have not depended on f2 in the frequency range 10-25 GHz, can be described successfully by this model. Finally, a figure of merit is proposed to evaluate material quality for high-Tc superconductors from the values of electron densities and momentum relaxation time determined by the present model.

In order to explain the temperature and frequency characteristics of high-Tc superconductors, a new model is proposed, which will be called the improved three-fluid model, where the momentum relaxation time τ is assumed to depend on temperature in the superconducting and normal states, respectively, although τ has been assumed to be independent of temperature for the conventional three-fluid model. According to this model, the complex conductivity σ1jσ2 and the surface impedance ZsRsjXs, where Rs is the surface resistance and Xs is the surface reactance, are expressed as a function of temperature. The temperature dependences of Zs and for a YBCO bulk estimated using this model agree very well with ones measured by the dielectric-loaded cavity method in room to cryogenic temperature. In particular, a peak of σ1 observed just below the critical temperature Tc in experiments, appeared in the calculated results based on this model. This phenomenon has been already known in the BCS theory. Thus, it is verified that this model is useful to explain the microwave characteristics of high-Tc superconductors in room to cryogenic temperature. On the other hand, the residual normal electron density nres4.2541023 m-3 and the total electron density nt7.3081024 m-3 are obtained by calculation. The ratio nres/nt0.058 can be used as figure of merit to evaluate material quality of high-Tc superconductors; thus it means that there is 5.8% nonpairing electron in this YBCO bulk.