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 ${\sigma }_c$ 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., ${\sigma }_{ab}/{\sigma }_c={\ell }_{ab}^2/{\ell }_c^2$. 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 $YB{a}_{2}C{u}_3{O}_x$ ($6.35<x<6.93$) 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 $\bar{\ell }$.

5 pages, 2 figures. To be published in J. Low Temp. Phys. Proceedings of MOS-99, Stockholm. Prompted by inquiries from readers, several clarifications are introduced: Temperature range over which data were taken is indicated; a misleading typo in the sentence at the bottom of page 3 is corrected; a few minor grammatical changes have been made