Role of interlayer coupling on the isotope effect in layered high-Tc cuprate superconductors

The present work deals with the study of the role of interlayer coupling on the isotope effect in high-Tc layered cuprate superconductors. For this purpose, we have considered two-layer tight-binding model that includes the intralayer attractive BCS type interactions and interlayer coupling in the form of single particle and Josephson Cooper pairing tunneling. Such a model calculation will be applicable for the high-Tc cuprate system like YBa2Cu3O7-x, having two CuO2 plane per unit cell, and also several other cuprate materials and may be extended for multilayer cuprate systems. To calculate the isotope effect coefficient (α), we derive the expression for the superconducting order parameter within the BCS mean field. We find that the isotope effect coefficient (α) increases with single particle tunneling but is independent of the Josephson Cooper tunneling. Finally, we have explained our theoretical results on isotope effect coefficient in the light of existing experimental observations