Superconducting pairing in the singlet band of the Emery model

The pairing due to electron-phonon and exchange interaction in the two-band Emery model is considered. The Emery model is reduced to an effective singlet-triplet problem. The Eliashberg-equations are formulated in terms of Hubbard operators for the singlet band. The dependence of the critical temperatureT_c on the number of holesn in the doped CuO₂ plane has been calculated. The electron-phonon coupling gives rise to s-wave pairing with a maximum inT_c atn1.2. It corresponds to a maximum in the density of states for a doping value ofn=1.24. The anisotropic electron-electron coupling due to the exchange interaction produces extended s-wave pairing with a maximum atn1.05 and d-wave pairing with a maximum atn1.2.