Resumo: We study the evolution from the weak coupling Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) at strong coupling in a two-band superconductor with orbitals ofopposite parity coexisting at a common Fermi surface in the metallic state. We analyze, independently,
the intra and the interband interactions where, in the former, hybridization destroys superconductivity and in the latter it plays a role similar to spin-orbit interaction in fermionic
spinor gases, enhancing the interband pairing and opening the possibility for driving the BCSBEC crossover. In multi-band superconductors the mass difference of the interacting fermions is also a relevant parameter to be considered and we show that the interband crossover is favored in systems with one dispersive and one flat band. Starting with a mean-field analysis, at both zero and finite temperatures, we investigate the crossover induced by an odd-parity hybridization.
The divergence in the interband critical temperature at the strong coupling limit is corrected with the inclusion of the thermal pair-fluctuations in a one-loop approximation. We then calculate the dependence of the condensation temperature on the microscopic parameters, namely hybridization,
scattering length and mass anisotropy. Finally we show that a smooth interband BCS-BEC crossover can indeed be attained via hybridization.