A phenomenological model including interlayer pairing interactions is proposed for high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors. Modified Eliashberg equations corresponding to the model are derived and numerically solved. The results show that the trends of ${\mathit{T}}_{\mathit{c}}$’s for known high-${\mathit{T}}_{\mathit{c}}$ materials can be described reasonably well by mechanisms including (in addition to the phonon interactions) nonphonon, intralayer- and interlayer-pairing interactions. The calculated gap values (3.6≲2${\mathrm{\Delta }}_0$/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$≲4.2) do not deviate significantly from the canonical BCS value of 3.5. This model can be applicable to layer-structured superconductors in general, whether they are high-${\mathit{T}}_{\mathit{c}}$ or low-${\mathit{T}}_{\mathit{c}}$ superconductors.

• Received 8 July 1991

DOI:https://doi.org/10.1103/PhysRevB.45.8007