Two-fluid interpretation of the microwave conductivity of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

The use of the two-fluid model for analyzing the microwave conductivity of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is critically appraised for s-wave and d-wave models and for weak and strong scattering, in the light of published results on single crystals, and of results here presented on high-quality epitaxial films and powders doped with Zn and Co. It is argued that the normal electrons in the best samples show nonlocal conductivity (λ<ℓ below 40 K), and that this provides a natural explanation of the low-temperature behavior of the measured surface impedance. If correct this model is firmly in favor of d-wave pairing. Evidence is shown that some 10% of electrons remain normal at T=0 in good films and 50% or more in heavily doped powders, in states which may or may not be localized. This behavior is associated with a ${\mathrm{T}}^2$ term in the temperature dependence of λ and is in accord with recent calculations of the effects of strong scattering impurities. It is argued that in the superconducting state transport between localized states is not necessarily associated with hopping conduction, because of the effects of Andreev reflection.