Superconductivity in homologous cuprate series: deep oscillations of   pairing Coulomb potential
  Kinematic constraint arising in the case of superconducting pairing with large momentum results in a cutoff of the screened Coulomb potential excluding large momentum transfers. This leads to a pairing potential oscillating in the real space that ensures a rise of bound singlet pairs. In multilayer cuprates, there is strong Coulomb interaction between particles composing the pair not only in the same cuprate layer but in the neighboring layers as well. In the framework of such a scenario, we explain a universal dependence of the superconducting transition temperature on the number of layers in the unit cell observed in homologous cuprate families. 
V.I. Belyavsky and Yu.V. Kopaev