The selected thermodynamic properties of the strong-coupled superconductors in the van Hove scenario

In the present paper, the exact numerical solutions of the Eliashberg equations within the van Hove scenario are obtained. The order function, the wave function renormalization factor, the energy shift function and the chemical potential are calculated. It is shown that the van Hove singularity change considerably the relationship between the order function and the occupation number. In particular, the order function have strong maximum in hole-doped region. Additionally, the critical temperature is calculated. It is shown that the observed maximum for the order function in hole-doped region induces a very high value of the critical temperature despite the fact that superconductivity originates from phonon-induced pairing. Finally, the ratio of the zero temperature energy gap to the critical temperature is found.