Cuprate Superconductivity: Dependence ofTcon thec-Axis Layering Structure

Without relying on any “model” of the in-plane behavior of the electrons in either the normal or the superconducting state, I show that for identically doped members of the same homologous series, as a result of the interplane Coulomb interaction, the difference $\Delta T_c^{\left(n\right)}$ of the transition temperature for the $n$th member from the single-layer value is given by $\Delta T_c^{\left(n\right)}=\mathrm{const}\times (1-1/n)$. On taking the constant from experiment, I predict large changes in the electron-energy-loss spectroscopy and optical properties in the midinfrared regime on entering the superconducting state, and further infer that the basic mechanism of superconductivity in the cuprates has a large contribution from the small- $q$ regime.