Experimental studies of the high-temperature superconducting cuprates using thermal difference reflectance spectroscopy

We report the results of a study of the temperature-dependent thermal difference reflectance (TDR) spectra of five different high-temperature superconducting cuprates, Tl{dollar}rmsb2Basb2Casb2Cusb3Osb{lcub}10{rcub}{dollar}, Tl{dollar}rmsb2Basb2CaCusb2Ossb8{dollar}, (BiPb){dollar}rmsb2Srsb2Casb2Cusb3Osb{lcub}10{rcub}{dollar}, HgBa{dollar}rmsb2CaCusb2Osb6{dollar} and YBa{dollar}rmsb2Cusb3Osb7{dollar}. Thermal difference reflectance spectroscopy is a technique by which it is possible to measure the temperature-dependent changes in a material's reflectance to 0.005%. By measuring the TDR spectra of the cuprate superconductors at several temperatures above and below each material's critical temperature, it is possible to gain information on the material's normal state optical parameters, and on the energy-dependence of the electron-boson coupling function that is responsible for superconductivity.; From the TDR spectta collected at room temperature, the value of the screened plasma frequency, {dollar}tildeomegasb{lcub}rm p{rcub}{dollar}, for each material has been graphically determined. The values for {dollar}tildeomegasb{lcub}rm p{rcub}{dollar} fall between 0.9 and 1.5 eV and are in good agreement with literature values. From the normal state TDR spectra collected at several temperatures, it has been found that the amplitude of the characteristic optical structure near the screened plasma frequency of each sample varies approximately linearly with temperature, T, indicating that the temperature-dependent normal state scattering rate in these materials scales with temperature as T{dollar}sp2{dollar}.; From the TDR spectra collected above and below the critical temperature of each sample, the superconducting to normal state reflectance ratio, R{dollar}sb{lcub}rm S{rcub}{dollar}/R{dollar}sb{lcub}rm N{rcub}{dollar}, has been obtained. In all of these spectra, there are significant deviations from unity in R{dollar}sb{lcub}rm S{rcub}{dollar}/R{dollar}sb{lcub}rm N{rcub}{dollar} at photon energies on the order of 2.0 eV. Both the temperature dependence and location of this structure in the R{dollar}sb{lcub}rm S{rcub}{dollar}/R{dollar}sb{lcub}rm N{rcub}{dollar} spectra may be described by solving the Eliashberg integral equations with an electron-boson coupling function that includes both an electron-phonon interaction and a high-energy electron-boson interaction. This high energy interaction is located at approximately the energies of known charge transfer excitations in these materials ({dollar}sim{dollar}2.0eV). We find remarkably good agreement between the experimental data and the results of our calculations based upon this description of the superconducting state.