Is There a Unified Description of Conductivity of Layered Cuprates ?

Abstract

We present a novel approach to the analysis of the normal state in-plane $\sigma _{ab}$ and out-of-plane σ_c conductivities of anisotropic layered crystals such as oxygen deficient YBa ₂ Cu ₃ O _x . It can be shown that the resistive anisotropy is determined by the ratio of the phase coherence lengths in the respective directions; i.e., $\sigma _{ab} /\sigma _c = \ell _{ab}^2 /\ell _c^2$. From the idea that at all doping levels and temperatures T the out-of-plane transport in these crystals is incoherent, follows that $\ell _c$ is T-independent, equal to the spacing $\ell _0$ between the neighboring bilayers. Thus, the T-dependence of $\ell _{ab}$ is given by the measured anisotropy, and $\sigma _{ab} (\ell _{ab} )$ dependence is obtained by plotting $\sigma _{ab} {\text{ }}vs{\text{ }}\ell = {\text{ (}}\sigma _{ab} /\sigma _c )^{1/2} \ell _0$.The analysis of several single crystals of YBa ₂ Cu ₃ O _x (6.35 < x < 6.93) shows that for all of them $\sigma _{ab} (\ell )$ is described by a universal dependence $\sigma _{ab} /\overline \sigma = f(\ell /\overline \ell )$ with doping dependent parameters $\overline \sigma {\text{ }}and{\text{ }}\overline \ell$.