Influence of pseudo-gap and interlayer coupling on isotope effect in bilayer cuprate superconductors

Abstract The present investigations deal with the study of the isotope effect in bilayer cuprate superconductors. We have considered the BCS-effective Hamiltonian that includes the intra and inter-layer kinetic energies and in plane attractive interaction responsible for pairing in these systems. In order to look for pseudo-gap having momentum dependence of the form of d-wave superconducting order parameter, a pseudo-gap order parameter is also introduced in the in-plane quasi-particle energy. Such a model calculation can be applicable for the high Tc cuprates like Bi2Sr2CaCu2O8+x having two CuO2 planes per unit cell and also for several other cuprate systems with a possibility to extend for the multi-layer cuprates. Employing Green's function formalism, we obtain the expressions for the superconducting order parameter and hence the isotope effect coefficient as a function of interlayer coupling, transition temperature and pseudo-gap order parameter. On the basis of numerical computation, we have pointed out that isotope effect increases due to coupling between the planes and decreases with the transition temperature. The presence of phenomenological pseudo-gap parameter in the quasi-particle spectrum enhances the isotope effect. These results are viewed in terms of recent experimental works on isotope effect in layered cuprate superconductors.