Influence of the van Hove singularity on the specific heat jump in BCS superconductors

Within the weak-coupling BCS scheme we derive a general form of the coefficients in the Ginzburg-Landau expansion of the free energy of a superconductor for the case of a Fermi level close to a van Hove singularity (VHS). A simple expression for the influence of the VHS on the specific heat jump is then obtained for the case where gaps for different bands are distinct but nearly constant at the corresponding sheets of the Fermi surface.