Relationship Between Conductivity and Phase Coherence Length in Cuprates

Abstract

The large ($10^2-10^5$) and strongly temperature dependent resistive anisotropy $\eta =({\sigma }_{ab}/{\sigma }_c{)}^{1/2}$ of cuprates perhaps holds the key to understanding their normal state in-plane ${\sigma }_{ab}$ and out-of-plane ${\sigma }_c$ conductivities. It can be shown that $\eta$ is determined by the ratio of the phase coherence lengths ${\ell }_i$ in the respective directions: ${\sigma }_{ab}/{\sigma }_c={\ell }_{ab}^2/{\ell }_c^2$. In layered crystals in which the out-of-plane transport is incoherent, ${\ell }_c$ is fixed, equal to the interlayer spacing. As a result, the T-dependence of $\eta$ is determined by that of ${\ell }_{ab}$, and vice versa, the in-plane phase coherence length can be obtained directly by measuring the resistive anisotropy. We present data for hole-doped $YB{a}_{2}C{u}_3{O}_y$ ($6.3<y<6.9$) and $Y_{1-x}P{r}_{x}B{a}_{2}C{u}_3{O}_{7-\delta }$ ($0<x\le 0.55$) and show that ${\sigma }_{ab}$ of crystals with different doping levels can be well described by a two parameter universal function of the in-plane phase coherence length. In the electron-doped $N{d}_{2-x}C{e}_{x}Cu{O}_{4-y}$, the dependence ${\sigma }_{ab}(\eta )$ indicates a crossover from incoherent to coherent transport in the c-direction.

5 pages, 2 figures

Cited by in corpus (1)

• Phenomenology of Conduction in Incoherent Layered Crystals