Anisotropic resistivity ofYBa2Cu4O8: Incoherent-to-metallic crossover in the out-of-plane transport

The resistivities of high-quality single crystals of ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ have been measured along all three crystallographic axes up to 450 K. Both the in-plane and out-of-plane resistivities show a distinct change in behavior on cooling from high temperatures. The chain resistivity ${\rho }_{\mathrm{chain}}\mathrm{}\left(T\right),$ by contrast, obeys a $T^2$ law over the entire temperature range. The $c-$axis resistivity ${\rho }_c\mathrm{}\left(T\right)\mathrm{}$ is almost $T$ independent at high $T,$ but as the temperature is reduced, the slope $d{\rho }_c/dT$ gradually increases and the $c-$axis transport crosses over from incoherent to metallic, implying the onset of three-dimensional conductivity at low $T.\mathrm{}$ These measurements reveal that the nonmetallic behavior of ${\rho }_c\mathrm{}\left(T\right)\mathrm{}$ in underdoped cuprates is not universal.