Dependence of the gap-ratio on the Fermi level shift in a van Hove superconductor

To understand the origin of high temperature superconductivity model based on the close proximity of the Fermi level to a quasi-two-dimensional Van Hove Singularity (VHS) in the density of states has been suggested. Here we present our study of the dependence of the zero temperature gap to the critical temperature for s- and d-wave superconductors on the Fermi level shift (delta) from the VHS within the BCS theory. Exact numerical calculations for the s and d gap ratios are carried out and approximate analytic expressions for the ratio are given. We find that the maximum gap ratio occurs at delta = 0, and it decreases symmetrically with increasing delta.