Role of bosonic modes in the mechanism of high temperature Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ superconductors using ultrafast optical techniques

Using ultrafast optical techniques, we probe the hole-doping dependence of the electron-boson coupling constant $λ$ in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$. In the overdoped region, we observe a correlation between ($λ$) and the superconducting transition temperature $T_{c}$. Upon performing the McMillan analysis, however, we find that $λ$ is too small to explain the high $T_{c}$'s, and that the Coulomb pseudopotential $μ^{\ast}$ is negative. Our analysis therefore reveals two components in the mechanism of high-$T_{c}$ superconductivity -- a dominant pre-existing pairing interaction, together with a weaker electron-phonon interaction that fine-tunes $T_{c}$.