Critical temperature in high-T_c layered superconductors: dependence on the number of interacting conducting layers per unit cell

Abstract

The generalized BCS pairing thoery for layered superconductors is used to investigate the dependence of the transition temperature T_c on the number N of interacting conducting Cu-O layers in any unit cell. The coupling constants, which describe intralayer and interlayer interactions in these layers where the Cooper pairing is assumed to take place, are explicity related to the microscopic polarization functions of all layers in the unit cell, including the insulating layers. With reasonable interlayer couplings it is possible to understand the experimental values of T_c in many of the high-T_c compounds discovered recently. One can indeed increase T_c as a function of N, but we find T_c(∞) to be less than 150K in polytypes of the [-(CuO₂)_N-] class, as well as in the 1:2:3 class polytypes [-(CuO₂)-(CuO-CuO₂)_n-], N=2+1. This is based on the approximation involving only up to the nearest neighbour conducting layer couplings and the use of experimental results for T_c in various thallium, bismuth and 1:2:3 compounds. A much higher T_c(∞) is possible only of the single-layer T_c(1) is high (>90 K) and interlayer couplings are significant.