The conceptual idea behind the electron-electron pairing mediated by an arbitrarily small attractive interaction plays a central role in the superconducting state. However, in these classical superconducting systems, the screened Coulomb potential is entirely suppressed by the phonon-driven attractive electron-electron interaction. We aim to examine the superconducting pair formation in the s-wave channel from a Coulomb correlated parental normal phase itself and later it has also been applied to anti-symmetric p-wave, d-wave and multi-band pairing channels.

A theoretical methodology for exploring the conventional Bardeen-Cooper-Schrieffer (BCS) pairing instability for superconductivity from a correlated normal phase for all possible degrees of many-body correlation, has been developed. The Gutzwiller projection scheme with a correlation parameter has been used to generate the BCS pairing state. The non-trivial commutation relation of the BCS pairing operator and the Gutzwiller projection operator leads to two distinct s-wave superconducting pairing scenarios. These two pairing scenarios are feasible under different experimental conditions.