Oxygen Isotope Effect in Bi$_{2}$Sr$_{2}$Ca$_{n-1}$Cu$_{n}$O$_{2n+4+\delta}$ ($n=1,2,3$) Single Crystals

We report measurements of the oxygen isotope effect in Bi{sub 2}Sr{sub 2}Ca{sub n-1}Cu{sub n}O{sub 2n+4+{delta}} (n=1, 2,3) single crystals. For optimally doped materials the isotope exponent is found to decrease with increasing the number of CuO2 layers in a manner of inversely correlating with the superconducting transition temperature in this homologous family. This behavior is in contrast to the general belief that the isotope effect can be negligible for the optimally doped cuprates. Our results highlight the important role played by phonons and interlayer coupling in the high-temperature superconductivity.