Investigation of fermionic pairing on two- dimensional tight binding lattice under phonon and electronic mechanisms within a Fermi liquid-like scenario and possible application to superconductivity in over doped cuprates

Cooper's original one pair problem in continuum is revisited here corresponding to a two- dimensional lattice of tight binding nature, with an aim to investigate superconductivity in quasi two dimensional systems. Both phonon and exciton mediated attraction in a passive Fermi liquid background are considered as possible pairing mechanism, with the non trivial energy dependence of the electronic density of states in the form of Van Hove singularity, taken into account in the calculation in a rigorous way. Some of the observed electronic properties in the normal phases of quasi two- dimensional cuprate superconductors in their over doped regions are used for the developement of the formalism and calculations. The results of our calculations show that a realistic fermionic pair formation is indeed possible, in conformity with more sophisticated treatment like Eliashberg theory. The estimates for various physical properties like the coherence length and the coupling constant from our theoretical calculations agree quite well with those from both Eliashberg theory based calculations as well as the weak coupling treatment and experiments. Furthermore, electronic mechanism turns out to be the more likely candidate for pair formation from our calculations in the overdoped phase.