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

We investigate the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover in a two-band superfluid Fermi gas with an energy shift between the bands. When the intraband coupling in the cold (first) band is fixed as weak, we find that in the case of vanishing pair-exchange interband coupling and in the strong-coupling limit of the hot (second) band the system undergoes a transition to a single-component configuration with a full suppression of the first energy gap and a full redistribution of particles between bands. For nonvanishing pair-exchange interband coupling we reveal a nonmonotonic dependence of the energy gap in the first band vs intraband coupling in the second band, with the presence of a hump. In the case of weak interband coupling, the system shows a significant amplification of the intrapair correlation length of the condensate in the first band in the strong-coupling regime of the second band, which clearly indicates the coexistence of giant Cooper pairs and a bosonic condensate even for nonzero temperatures. This can lead to a nonmonotonic temperature dependence of the second energy gap with a peak. The here predicted coexistence of giant Cooper pairs and bosonic molecules can be verified by means of the visualization of vortex cores in two-component atomic condensates as well as in some iron-based superconductors.