C-axis Transport in Bilayer Cuprates and Relation to Pseudogap

We consider the effect of interband transitions on the c-axis conductivity, DC resistivity, and thermal conductivity in a plane-chain bilayer model of a cuprate. The relation between the c-axis resistivity and thermal conductivity is governed by the Wiedemann-Franz law. When the perpendicular hopping matrix element between chain and plane ($t_\perp$) is small, the c-axis DC resistivity shows a characteristic upturn as the temperature is lowered and the infrared conductivity develops a pseudogap. As $t_\perp$ is increased, intraband transitions start to dominate and a more conventional response is obtained. Analytical results for a simple plane-plane bilayer are also given, including the frequency sum rule of the optical conductivity.