Modification of the isotope effect by the van Hove singularity of electrons on a two-dimensional lattice

We discuss the problem of phonon-induced superconductivity of electrons on a two-dimensional lattice. Analytical expressions for the superconducting transition temperature and the isotope coefficient have been derived for the case that the Fermi level is close to the van Hove singularity. We have considered the weak- and strong-coupling cases. Our results show that in the presence of the van Hove singularity the isotope coefficient can take on small values despite the fact that superconductivity originates from phonon-induced pairing.