Pseudogap and Charge Dynamics inCuO2Planes in YBCO

We report on the infrared conductivity of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3\mathrm{O}{}_x$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_4\mathrm{O}{}_8$ crystals with different oxygen content and Zn doping. We find a correlation between the structure of the scattering rate spectra $1/{\tau }_a^{*}(\omega ,T)$ in the ${\mathrm{CuO}}_2$ planes and the pseudogap that develops in the c-axis conductivity of underdoped samples for $T<\mathrm{}{T}^{*}=140\mathrm{}–250\mathrm{K}$. In the pseudogap state, the scattering rate is depressed at low frequencies and follows an ${\omega }^{2\pm 0.3}$ law for $\omega <400\mathrm{}{\mathrm{cm}}^{-1\mathrm{}}$. When the c-axis pseudogap is suppressed, either by an increase of temperature above $T^{*}$ or by a substitution of Cu with Zn, the spectra of $1/{\tau }_a^{*}(\omega ,T)$ revert to the nearly linear $\omega$ dependence of the optimally doped compounds.