Is There a Unified Description of Conductivity of Layered Cuprates ?

We present a novel approach to the analysis of the normal state in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ 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 $\sigma_{ab}$ vs $\ell=(\sigma_{ab}/\sigma_c)^{1/2}\ell_0$. 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 $\sigma_{ab}/\bar\sigma =f(\ell/\bar\ell)$ with doping dependent parameters $\bar\sigma$ and $\bar\ell$.