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 T_c cuprates like Bi₂Sr₂CaCu₂O_8+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.

目前的研究涉及双层铜酸盐超导体中同位素效应的研究。我们已经考虑了 BCS 有效哈密顿量，其中包括层内和层间动能以及负责这些系统中配对的平面内吸引力相互作用。为了寻找具有d波超导阶参数形式的动量依赖性的赝隙，在面内准粒子能量中还引入了赝隙序参数。这种模型计算适用于高 T _c铜酸盐，如 Bi ₂ Sr ₂ CaCu ₂ O _8+x具有两个 CuO ₂每个晶胞的平面以及其他几种铜酸盐系统，可以扩展到多层铜酸盐。利用格林函数形式，我们获得了超导有序参数的表达式，从而获得了作为层间耦合、转变温度和伪间隙有序参数的函数的同位素效应系数。在数值计算的基础上，我们指出同位素效应由于平面之间的耦合而增加，并随着转变温度的增加而降低。准粒子光谱中现象学伪间隙参数的存在增强了同位素效应。这些结果是根据最近关于层状铜酸盐超导体中同位素效应的实验工作来看待的。