Role of metallic layers in high temperature superconductors and calculation of citrical temperature

The purpose of this work is to investigate the role of metallic layers in high temperature superconductors. A model consisting of three layers in one unit cell is developed. By assuming the existence of various layer coupling (coherent pair transition and direct hopping) between layers, one finds that the bounding layers play significant roles in renormalizing the interaction constants of the system. Within the framework of this model, the major results and predictions are as follows: the introduction of a small interlayer hopping matrix element always reduces the critical temperature Tc , the Josephson like coupling between layers always enhances Tc, possible proximity effect in the neighbouring layer plays an important role in the enhancement of Tc. Our formulas cover the cases of one superconducting layers, two superconducting layers, one insulating layer between two superconducting layers, three similar superconducting layers and one superconducting layer between two insulating layers.