Thermal-difference reflectance spectroscopy of the high-temperature cuprate superconductors

The temperature-dependent thermal-difference reflectance (TDR) spectra of thin-film samples of ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$, (BiPb${)}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$, ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$, and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ have been measured for photon energies between 0.3 and 4.5 eV at temperatures above and below each material’s superconducting critical temperature. The amplitude of the characteristic optical structure near the screened plasma frequency of each sample in the normal-state TDR spectrum varies approximately linearly with temperature, T, indicating that the temperature-dependent optical scattering rate in these materials scales with temperature as ${\mathit{T}}^2$. From the TDR spectra collected above and below the critical temperature of each sample, the superconducting to normal-state reflectance ratio, ${\mathit{R}}_{\mathit{S}}$/${\mathit{R}}_{\mathit{N}}$, has been obtained. In all of these spectra, there are significant deviations from unity in ${\mathit{R}}_{\mathit{S}}$/${\mathit{R}}_{\mathit{N}}$ at photon energies on the order of 2.0 eV. This optical structure cannot be accounted for using the conventional Mattis-Bardeen description of the optical properties of a superconductor or its strong-coupling extension where electron-pairing interactions are limited to energies less than 0.1 eV. However, both the temperature and energy dependence of the structure in the ${\mathit{R}}_{\mathit{S}}$/${\mathit{R}}_{\mathit{N}}$ spectra may be adequately described within Eliashberg theory with an electron-boson coupling function which consists of both a low-energy component (1996 The American Physical Society.