Superconductivity in the strong coupling limit: Van Hove singularity and extended saddle point singularity scenario

The effect of orthorhombic distortion and second nearest neighbor hopping on the transition temperature (T-c) and the isotope-shift exponent (alpha) have been studied for a two dimensional system, within the framework of Eliashberg formalism in the van Hove singularity scenario. The behavior of T-c and alpha have been discussed for the case of extended saddle point singularity. A comparison of the strong coupling theory results is made with the results of weak coupling theory. From our study it reveals that the effect of singularity in the density of states (DOS) in the strong coupling limit is not so significant as that in weak coupling case.