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 T 2 . From the TDR spectra collected above and below the critical temperature of each sample, the superconducting to normal-state reflectance ratio, R S /R N , has been obtained. In all of these spectra, there are significant deviations from unity in R S /R 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 R S /R N spectra may be adequately described within Eliashberg theory with an electron-boson coupling function which consists of both a low-energy component ͑Ͻ0.1 eV͒ and a high-energy component located between 1.6 and 2.1 eV.
We report the results of a study of the temperature-dependent thermal difference reflectance spectra of T12Ba2Ca2Cu3010. At temperatures below T"afeature emerges in the spectra with an integrated amplitude that scales as b, o(T), where ho(T) is the temperature-dependent superconducting gap. The temperature dependence and location of this feature can be described by an Eliashberg model with a coupling function that includes both an electron-phonon interaction and an interaction located at -1.6 eV. We find remarkably good agreement between theory and experiment based upon this description of the superconducting state.PACS numbers: 74.25.6z, 74.20.Mn, 74.72.Fq The most fundamental problem of high-T, superconductivity is the determination of the mechanism responsible for the high critical temperatures observed in the cuprate superconductors.
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