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The properties of the superconducting and the anomalous normal state were described by using the Eliashberg method. The pairing mechanism was reproduced with the help of the Hamiltonian, which models the electron‐phonon and the electron‐electron‐phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function (φ), the wave function renormalization factor ( Z ), and the energy shift function (χ), was derived. It was proven that for the sufficiently large values of the EEPh potential, the doping dependence of the order parameter (   φ  /  Z   ) has the analogous course to that observed experimentally in cuprates. The energy gap in the electron density of states is induced by  Z  and χ ‐ the contribution from φ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature.

Pseudogap in the Eliashberg approach based on electron‐phonon and electron‐electron‐phonon interaction