Comment on the linear resistivity of high-temperature superconducting compounds

Abstract

We report calculations of the phonon-induced electrical resistivity ρ(T) of YBa₂Cu₃O₇ using Allen's expression for inverse transport relaxation time τ_ph ⁻¹. ρ(T) is found to be a quasi-linear function of T(ρ ∞ T ^0.98) for T ≥ 90 K, i.e. for T ≥ T _c. The calculation does not take into account Umklapp scattering, which is likely to be important in the high-temperature superconductors (HTSCs) because of the low-lying optical phonon branches found in these compounds. Therefore, linear T behaviour of ρ(T) might well extend substantially below the transition temperatures of most HTSCs. Results for ρ (T) for a Debye-Einstein model of HTSCs (which gives realistic results for c_u (T) and θ_Debye(T)) show linear behaviour of ρ(T) starting at even lower tempertures (T ≥ 30 K). We conclude from these results that linear T behaviour of the resistivity of HTSCs is fully compatible with the Bloch-Grineisen theory of resistivity in ordinary metals, and is, in itself, not an indication that a non-phonon mechanism must be underlying the phenomenon of high-temperature superconductivity.