Cooper-pair size and binding energy for unconventional superconducting systems

The main proposal of this paper is to analyze the size of the Cooper pairs composed by unbalanced mass fermions from different electronic bands along the BCS-BEC crossover and study the binding energy of the pairs. We are considering an interaction between fermions with different masses leading to an inter-band pairing. In addiction to the attractive interaction we have an hybridization term to couple both bands, which in general acts unfavorable for the pairing between the electrons. We get first order phase transitions as the hybridization break the Cooper pairs for the the $s$-wave symmetry of the gap amplitude. The results show the dependence of the Cooper-pair size as a function of the hybridization for $T=0$. We also propose the structure of the binding energy of the inter-band system as a function of the two-bands quasi-particle energies.