Simplified Approach Of Investigation Of Binding Energy For Fermionic Pairing In Two Dimensional Fermi Liquid Type Superconducting Materials At Finite Low Temperature

Relation between the binding energy of pair of fermions and the magnitude of the attractive interaction between them is investigated theoretically with the help of mean field approximation, for a two-dimensional (2D) Fermi liquid type superconducting material. Here the fermion pair has finite center of mass momentum (CMM). The fermion pair is considered to be formed in the presence of an active Fermi sea having multiple pairs with inclusion of the effect of Pauli exclusion principle, at finite low temperature. Our calculations show that coexistence of true bound state (TB) and Cooper pair state (CP) with various CMMs can occur only beyond a critical attractive interaction strength which is similar to the results obtained at T = 0 K[1]. We establish that Coopers pair state to true bound state crossover can be possible to achieve controlling the value of CMM of the fermion pairs. This could lead to the well-studied phenomena Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein Condensed (BEC) crossover and also the formation of incoherent pairs, under strong coupling regime. This throws a significant emphasis on the normal state anomalies seen in some of the exotic superconductors.