Using ultrafast optical techniques, we probe the hole-doping dependence of the electron-boson coupling constant $\lambda$ in Bi$_{ 2}$Sr$_{ 2}$CaCu$_{ 2}$O$_{ 8+\delta}$. In the overdoped region, we observe a correlation between ($\lambda$) and the superconducting transition temperature $T_{ c}$. Upon performing the McMillan analysis, however, we find that $\lambda$ is too small to explain the high $T_{ c}$'s, and that the Coulomb pseudopotential $\mu^{ \ast}$ 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 $T_{ c}$.
Categories: cond-mat.supr-con cond-mat.str-el