Conductivity and phase coherence length of single electrons in layered cuprates

We present a novel approach to the analysis of the normal-state in-plane σ_ab and out-of-plane σ_c conductivities of anisotropic layered cuprates with incoherent out-of-plane transport such as YBa₂Cu₃O_x (6.35 ⩽ x ⩽ 6.93) and Y_{1 − y}Pr_yBa₂Cu₃O_{7 − δ} (0.08 ⩽ y ⩽ 0.53). We show that the resistive anisotropy σ_ab/σ_c of these crystals is a measure of the in-plane phase coherence length ℓ_φ,ab. This result has two important implications: i) One can obtain experimentally the dependence of conductivity on phase coherence length σ_ab,c(ℓ_φ,ab). This σ_ab,c(ℓ_φ,ab)-dependence for different doping follows a universal scaling relationship. This universality of σ_ab,c(ℓ_φ,ab) for different doping is a direct experimental confirmation of the scaling hypothesis. ii) σ_ab/σ_c at a given temperature changes nonmonotonically with doping, reaching a maximum in the sample closest to the metal-insulator transition. We show that this result is a consequence of incoherent c-axis conduction.