Isotope effects and possible pairing mechanism in optimally doped cuprate superconductors

We have studied the oxygen-isotope effects on $T_c$ and in-plane penetration depth ${\lambda }_{\mathrm{ab}}\mathrm{}\left(0\right)\mathrm{}$ in an optimally doped three-layer cuprate ${\mathrm{Bi}}_{1.6}{\mathrm{Pb}}_{0.4}{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+y}$ ${(T}_c\sim 107\hspace{0.5em}\mathrm{K}).\mathrm{}$ We find a small oxygen-isotope effect on $T_c$ $({\alpha }_O=0.019),$ and a substantial effect on ${\lambda }_{\mathrm{ab}}\mathrm{}\left(0\right)\mathrm{}$ $\left[\Delta {\lambda }_{\mathrm{ab}}\mathrm{}\right(0)/{\lambda }_{\mathrm{ab}}\mathrm{}(0)=2.5\mathrm{}\pm 0.5\%].$ The present results along with the previously observed isotope effects in single-layer and double-layer cuprates indicate that the isotope exponent ${\alpha }_O$ in optimally doped cuprates is small while the isotope effect on the in-plane effective supercarrier mass is substantial and nearly independent of the number of the ${\mathrm{CuO}}_2$ layers. A plausible pairing mechanism is proposed to explain the isotope effects, high-$T_c$ superconductivity, and tunneling spectra in a consistent way.