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 $YB{a}_{2}C{u}_3{O}_x$. It can be shown that the resistive anisotropy is determined by the ratio of the phase coherence lengths in the respective directions; i.e., ${\sigma }_{ab}\mathrm{/}{\sigma }_c={\mathrm{\ell }}_{ab}^2\mathrm{/}{\mathrm{\ell }}_c^2$. From the idea that at all doping levels and temperatures $T$ the out-of-plane transport in these crystals is incoherent, follows that ${\mathrm{\ell }}_c$ is T-independent, equal to the spacing ${\mathrm{\ell }}_0$ between the neighboring bilayers. Thus, the T-dependence of ${\mathrm{\ell }}_{ab}$ is given by the measured anisotropy, and ${\sigma }_{ab}({\mathrm{\ell }}_{ab})$ dependence is obtained by plotting ${\sigma }_{ab}$ vs $\mathrm{\ell }=({\sigma }_{ab}\mathrm{/}{\sigma }_c{)}^{1\mathrm{/}2}{\mathrm{\ell }}_0$. The analysis of several single crystals of $YB{a}_{2}C{u}_3{O}_x$ ($6.35<x<6.93$) shows that for all of them ${\sigma }_{ab}(\mathrm{\ell })$ is described by a universal dependence ${\sigma }_{ab}\mathrm{/}\bar{\sigma }=f(\mathrm{\ell }\mathrm{/}\bar{\mathrm{\ell }})$ with doping dependent parameters $\bar{\sigma }$ and $\bar{\mathrm{\ell }}$.