Resistivity of multiphase high-Tc superconductors

Resistivity versus temperature (ρ-T) behavior of high-T_c superconductors in the normal state was recently modeled semiempirically according to conventional electron hopping theory for mixed-valence metal oxides. One important feature of this work was the interpretation of a resistivity minimum (i.e., the transition between insulator and metal) in the temperature regime near T_c, based on the decrease of activation energies E_hop with increases in magnetic dilution reported in the NiO and CuO systems. Quantitative accuracy has now been established by fitting ρ-T data of the La_2-xSr_xCuO₄ and YBa₂Cu₃O₇ high-T_c compounds, which serve as the basis for interpreting the varying slopes of multiphase superconductors. Calculated curves fitted to reported experimental data show that the metallic slope (∂ρ/∂T≳0 above T_c) and the ρ-axis intercept of the linear extrapolation may be used to estimate the volume ratio of effective superconducting phase to normal phase within a particular specimen. From the application of this theory, it is determined that: (i) ρ-axis intercepts of single-phase superconductors are proportional to E_hop(1 - x)/x; (ii) normal phases cause increases in ρ, but decreases in slope of ρ(T)/ρ(300); and (iii) metallic slopes may be achieved with less than 10% effective volume of superconducting phase.