Investigation of fermionic pairing on tight binding lattice for low dimensional systems – Fermi liquid vs. Luttinger–Tomonaga liquid

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 in a passive Fermi sea-like background 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 in the normal phase of quasi one dimensional organic superconductors are used for the development of the formalism and calculations. The results of our calculations show that a realistic fermionic pair formation is indeed possible with some constraints, without any necessity at all of invoking Luttinger–Tomonaga liquid (LTL) theory. Similarities emerge in the physical properties of the electron pair formed from Cooper's treatment corresponding to continuum and ours, excepting the striking difference appearing in the form of occurrences of a maximum allowed band filling for pairing and of an upper bound of the pairing energy found in our approach.