Anisotropy of the optical conductivity of high-Tccuprates

The optical conductivity along $\left({\sigma }_{\mathrm{xx}}\right)$ and perpendicular $\left({\sigma }_{\mathrm{zz}}\right)$ to the planes is calculated assuming strong $k_{\Vert }$ dependence of the scattering rate and the c-axis hopping parameter. The closed analytical expressions for ${\sigma }_{\mathrm{xx}}\left(\omega \right)$ and ${\sigma }_{\mathrm{zz}}\left(\omega \right)$ are shown to be integrable at low and high frequencies. A large and qualitatively different frequency dependence for both polarizations follows directly from the model. The expression for ${\sigma }_{\mathrm{xx}}\left(\omega \right)$ has an effective scattering rate proportional to frequency, and can be easily generalized to provide a simple analytical expression, which may replace the Drude formula in the case of non-Fermi liquids.