Investigation of fermionic pairing on tight binding lattice for low dimensional systems

Cooper's original one pair problem in continuum is revisited here corresponding to a lattice of tight binding nature, with an aim to investigate superconductivity in low dimensional systems. An electronic type of boson mediated attraction is considered for the pairing mechanism with the non trivial energy dependence of the electronic density of states taken into account in the calculation in a rigorous way. Some of the very important electronic and optical properties of a class of one dimensional organic conductors are used for the development of the formalism and calculation. The result of our calculations show that fermionic pair formation is indeed possible with some constraints. Similarities emerge in the physical properties of the electron pair formed from Cooper's treatment and ours excepting the striking difference appearing in the form of occurrence of a maximum allowed band filling for pairing and of an upper bound of the pairing energy found in our approach.