Optical determination of the relation between the electron-boson coupling function and the critical temperature in high- Tc cuprates

We take advantage of the connection between the free-carrier optical conductivity and the glue function in the normal state, to reconstruct from the infrared optical conductivity the glue spectrum of ten different high- Tc cuprates revealing a robust peak in the 50-60 meV range and a broad continuum at higher energies for all measured charge-carrier concentrations and temperatures up to 290 K. We observe that the strong-coupling formalism accounts fully for the known strong temperature dependence of the optical spectra of the high- Tc cuprates, except for strongly underdoped samples. We observe a correlation between the doping trend of the experimental glue spectra and the critical temperature. The data obtained on the overdoped side of the phase diagram conclusively exclude the electron-phonon coupling as the main source of superconducting pairing.