Oxygen isotope effect in layered cuprate superconductors

The isotope effect has generally been believed to be important in providing information about the high-temperature superconductivity. We report systematic studies of the oxygen isotope effect in nearly optimally doped Bi$_{2}$Sr$_{2}$Ca$_{n-1}$Cu$_{n}$O$_{2n+4+\delta }$ (n=1,2,3) single crystals. We find that $\alpha $ decreases monotonically with increasing the number of CuO$_{2}$ layers in this series, which is considered as a result of the interlayer coupling effect. Our results suggest that a $d$-wave BCS equation with a phonon cutoff is able to provide a self-consistent explanation for both the Tc and $\alpha $ behaviors of cuprates covering the parameters of doping, CuO$_{2}$ layer, and compound. The proposed theoretical model is also used to predict the pressure dependence of the oxygen isotope exponent in the optimally doped YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ based on our measured Tc and Raman data. We find that $\alpha $ decreases with increasing pressure and becomes negative at some pressure. Such prediction is waiting for direct isotope measurements under high pressures.