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We have studied the oxygen-isotope effect on the superconducting transitiontemperature $T_{c}$ in overdopedY$_{1-x}$Ca$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ with $x$ = 0.10, 0.20, and0.25. We find the oxygen-isotope exponent $\alpha_{O}$ to be small ($\sim$0.02)for $x$ = 0.10 but substantial ($\sim$0.1) for $x$ = 0.20 and 0.25. The dopinglevel above which $\alpha_{O}$ increases sharply coincides with a quantumcritical point where the normal-state pseudogap starts to diminish. The presentisotope-effect experiments provide direct and quantitative constraints on thepairing mechanism of high-temperature superconductivity in cuprates.

Large oxygen-isotope shift above the quantum critical point of $Y_{1-x}Ca_xBa_2Cu_3O_{7-delta}$