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 co-existence 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.

对于二维（2D）费米液体型超导材料，理论上借助于平均场近似研究了成对的费米子的结合能与它们之间的吸引力相互作用的大小之间的关系。在此，费米对具有有限的质心动量（CMM）。费米对被认为是在有限的低温下，在具有多个波对的活跃费米海的存在下形成的，其中包括保利排斥原理的作用。我们的计算表明，只有在超出临界引力相互作用强度的情况下，才能发生真结合态（TB）和库珀对态（CP）与各种CMM的共存，这与在$Ť=0$K [1]。我们建立了库珀对状态到真实束缚状态的交叉可以实现对费米对的CMM值的控制。在强耦合机制下，这可能导致对Bardeen-Cooper-Schrieffer（BCS）到Bose-Einstein凝聚态（BEC）的交叉现象进行深入研究的现象，并且还会形成不相干的对。这极大地强调了在某些奇特的超导体中看到的正常状态异常。