Frequency- and temperature-dependent conductivity in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ crystals

The results of a systematic study of the optical properties of the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$-based insulators and superconductors are reported. Specifically, we present measurements and analysis of the optical reflectivity R of a series of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ crystals in the frequency range from 30 to 20 000 ${\mathrm{cm}}^{\mathrm{-}1}$ (4 meV to 2.5 eV), and temperature range from 10 to 270 K. From R we obtain the real part of the frequency-dependent optical conductivity σ(ω) by Kramers-Kronig analysis. In our discussion, we emphasize the development of structure and spectral weight in σ(ω) as the compounds change from insulators to high-${\mathit{T}}_{\mathit{c}}$ superconductors with varying O content or Al doping. We identify the free carrier, and interband components of σ(ω), and focus on the free-carrier component.