Optical Evidence of an Electronic Contribution to the Pairing Interaction in Superconducting ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$

We report the results of a study of the temperature-dependent thermal difference reflectance spectra of ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$. At temperatures below $T_c$, a feature emerges in the spectra with an integrated amplitude that scales as ${\Delta }_0^2\mathrm{}\left(T\right)\mathrm{}$, where ${\Delta }_0\mathrm{}\left(T\right)\mathrm{}$ 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.