Electron pairing in model with two overlapping bands

We consider the two-band Hubbard model, where electrons from different bands interact through an on-site one- and two-particle hybridization. The proposed Hamiltonian makes it possible to construct an effective theory and answer the question of the nature of pairing: conduction electrons form pairs due to two-particle hybridization of electrons from different bands, compensating for the direct Hubbard repulsion between conduction electrons. It is shown that an effective attraction between conduction electrons leads to $η$-pairing. The electron-electron pairing mechanism explains the presence of superconductivity at high temperatures experimentally observed in hydrogen-rich materials at high pressure.