Thermal conductivity and electrical resistivity of the Y- and Er-substituted 1:2:3 superconducting compounds in the vicinity of the transition temperature

The thermal conductivity and electrical resistivity of ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ sintered compounds have been measured to investigate the electron-phonon interaction in the vicinity of ${\mathit{T}}_{\mathit{c}}$ in these materials. The thermal conductivity was measured using the transient-plane-source technique. With the electrical-resistivity data and Wiedeman-Franz law, the magnitude of the free-carrier component of the thermal conductivity has been estimated to less than 15% of the measured thermal conductivity. The results in the normal state are interpreted in terms of two models. The first model is the ordinary electron-phonon transport theory applied to high-${\mathit{T}}_{\mathit{c}}$ superconductors, and the second model is the Bardeen-Rickayzen-Tewordt (BRT) theory of the lattice heat conduction in high-${\mathit{T}}_{\mathit{c}}$ superconductors. Both models suggest that the electron-phonon coupling varies from moderately weak to strong coupling depending on characteristic parameters of the considered material such as oxygen content, porosity, ${\mathit{T}}_{\mathit{c}}$ value, Δ${\mathit{T}}_{\mathit{c}}$, etc., all of which are directly related to the purity of the investigated samples. Furthermore, using this transient technique a dramatic increase of the thermal conductivity is observed below ${\mathit{T}}_{\mathit{c}}$ and the experimental results are in reasonable agreement with the prediction of the generalized BRT theory, adapting a weak coupling with scaled-BCS-gap formalism for the moderately-weak-coupling sample and a strong coupling s-wave-pairing formalism for the strong-coupling sample.