BCS-BEC crossover in a two-band superconductor with odd-parity hybridization

We study the crossover from the weak coupling Bardeen-Cooper-Schrieffer (BCS) state to Bose-Einstein condensation (BEC) at strong coupling in a two-band superconductor with orbitals of opposite parity coexisting at a common Fermi surface in the metallic state. In such systems hybridization can play a role similar to spin-orbit interaction in fermionic spinor gases, enhancing interband pairing and opening the possibility for driving the BCS-BEC crossover. Building on a mean-field analysis, we investigate the BCS-BEC crossover induced by a variation of the hybridization strength. We show that the relevant scale for the crossover depends strongly on the ratio of effective masses, with the crossover favored in systems with one dispersive and one flat band. Including the effect of thermal pair fluctuations in a one-loop approximation, we calculate the dependence of the critical temperature on the microscopic parameters in the strong coupling regime.