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We investigate Bardeen-Cooper-Schrieffer (BCS)- Bose-Einstein condensation(BEC) crossover in a two-band superfluid Fermi gas with an energy shift betweenthe bands. When the intraband coupling in the cold (first) band is fixed asweak, we find that in the case of vanishing interband interaction and in thestrong-coupling limit of the hot (second) band the system undergoes atransition to a single-component configuration with the full suppression of thefirst energy gap and with the full redistribution of particles between bands.For non-vanishing interband interaction we reveal the non-monotonic dependenceof the energy gap in the first band vs intraband coupling in the second bandwith the presence of a hump. In the case of weak interband coupling the systemshows a significant amplification of the intrapair correlation length of thecondensate in the first band in the strong-coupling regime of the second band,which clearly indicates the coexistence of giant Cooper pairs and a bosoniccondensate even for nonzero temperatures. This can lead to a non-monotonictemperature dependence of the second energy gap with a peak. Here predictedcoexistence of the giant Cooper pairs and bosonic molecules can be verified bymeans of the visualization of vortex cores in the two-component atomiccondensates as well as in some iron-based superconductors.

physical review. b./physical review. b

Coexistence of giant Cooper pairs with a bosonic condensate and  anomalous behavior of energy gaps in the BCS-BEC crossover of a two-band  superfluid Fermi gas