Dielectric tensor of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$: Experiment and theory

In this work we present measurements of the anisotropic optical response of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$. By using ellipsometry and reflectance measurements, we obtained all three components of the dielectric tensor in the energy range between 0.05 and 5.5 eV. We report the existence of a plasma edge for light polarized perpendicular to the ${\mathrm{CuO}}_2$ planes. For the in-plane optical response, Drude-Lorentz fits to our reflectance spectra show a behavior that differs qualitatively from that reported for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, namely that the scattering frequency for the carriers in the chain is smaller than for the plane carriers. We assign this to the stability of the chains against oxygen loss and disorder. We have isolated the contribution of interband transitions to the dielectric function and compare it to results from an ab initio calculation. For the computation of the one-electron states we used the linear-muffin-tin-orbital method in the atomic-sphere approximation. We find good agreement between the calculated and the measured spectra, hinting at the validity of the underlying one-electron local-density approximation. We give a microscopic explanation of the observed structure in the optical response and point out the main differences between the band structures of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ as they manifest themselves in the optical properties.