Thermal and electronic properties of rare-earth ${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathrm{x}}$ superconductors

We have measured the electrical resistivity, thermal conductivity, and specific heat of a series of high-temperature superconducting compounds of the form R${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, with R=Y, Eu, Gd, Dy, and Er. Our results show that the afore-mentioned physical properties are virtually identical for all samples considered. In particular, the molar specific heats are identical to within ±2% and exhibit Debye-type behavior. We observe a nearly constant thermal conductivity above $T_c$, but a rather sudden increase developes as the temperature is lowered below the critical temperature. The electrical resistivity is nearly linear in the normal state. Thermal and electrical conductivities indicate that for T>$T_c$, the predominant electron scattering mechanism is due to phonon interactions. Using electrical resistivity data and the Wiedemann-Franz law, we estimate the magnitude of the electronic component of the thermal conductivity to be an order of magnitude smaller than the measured thermal conductivity. We thus conclude that heat transport is predominantly by phonons. The enhancement of the lattice conduction below the critical temperature is understood as a reduction of carrier-phonon scattering as electrons condense into Cooper pairs. This lends support to standard Bardeen-Cooper-Schrieffer-type superconductivity. An estimate of the superconducting transition temperatures is made using the electron-phonon coupling constants and Debye temperatures deduced from the data which brackets the observed $T_c$ quite well. We discuss the thermal conductivity at very low temperature in terms of a phonon mean-free path limited by pores in the samples.