Apex oxygen and critical temperature in copper oxide superconductors: Universal correlation with the stability of local singlets

Electronic-energy-level structures of the layered Cu oxide compounds are drawn within the ionic model. Correlations between the level separations obtained and the superconducting critical temperature ${\mathit{T}}_{\mathit{c}}$ are examined for all families of the Cu oxide superconductors. It is proposed that the position of the energy level of the apex oxygen atoms is of primary importance for the electronic states of the ${\mathrm{CuO}}_2$ plane and governs the optimum ${\mathit{T}}_{\mathit{c}}$’s of all families of hole-carrier suprconductors. The pressure effect of ${\mathit{T}}_{\mathit{c}}$ is discussed within this framework. Based on cluster-model calculations, where the covalency neglected in the ionic model is fully taken into account, we argue that the role of the apex oxygen atoms is to prescribe the stability of local singlet states made of two holes in the Cu 3${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ and O 2${\mathit{p}}_{\mathrm{\sigma }}$ orbitals of the ${\mathrm{CuO}}_2$ plane, and thereby to control the maximum ${\mathit{T}}_{\mathit{c}}$ of each family.