Microscopic Bardeen-Cooper-Schrieffer formulation of the critical temperature of multilayer copper-oxide superconductors

We study superconductivity in multilayer copper oxides, in the frame of a realistic microscopic formulation. Solving the full temperature dependent BCS gap equations, we obtain a maximum in the transition temperature T_c for M = 3 or 4 CuO₂ layers in the unit cell for appropriate values of the interlayer tunneling (negative pair tunneling), and via the consideration of the doping imbalance between the inner and outer layers. This is the ubiquitous experimental result for Ca intercalated copper oxides, as opposed to other intercalating elements. Further, using a restricted set of parameters, we obtain an exact fit of T_c(M = 1–4) for five different Ca intercalated homologuous copper oxide families.