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 σc 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 $$\overline \sigma {\text{ }}and{\text{ }}\overline \ell $$ .