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 $σ_{ab}$ 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., $σ_{ab}/σ_c=\ell_{ab}^2/\ell_c^2$. 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 $σ_{ab}(\ell_{ab})$ dependence is obtained by plotting $σ_{ab}$ vs $\ell=(σ_{ab}/σ_c)^{1/2}\ell_0$. The analysis of several single crystals of $YBa_{2}Cu_{3}O_{x}$ ($6.35<x<6.93$) shows that for all of them $σ_{ab}(\ell)$ is described by a universal dependence $σ_{ab}/\barσ=f(\ell/\bar\ell)$ with doping dependent parameters $\barσ$ and $\bar\ell$.