Band-edge BCS–BEC crossover in a two-band superconductor: physical properties and detection parameters

Superconductivity in iron-based magnesium diborides and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity of the chemical potential to the edge of one of the bands. Here we study the simplest theoretical model which accounts for the BCS-BEC crossover in a two-band superconductor, considering tunable interactions and tunable energy separations between the bands. Mean-field results for condensate fraction, correlation length, and superconducting gap are reported in typical crossover diagrams to locate the boundaries of the BCS, crossover and BEC regimes. When the superconducting gap is of the order of the local chemical potential, superconductivity is in the crossover regime of the BCS-BEC crossover and the Fermi surface of the small band is smeared by the gap opening. In this situation, small and large Cooper pairs coexist in the total condensate, which is the optimal condition for high-T-c superconductivity. The ratio between the gap and the Fermi energy in a given band results in the best detection parameter for experiments to locate the system in the BCS-BEC crossover. Using available experimental data, our analysis shows that iron-based superconductors have the partial condensate of the small Fermi surface in the crossover regime of the BCS-BEC crossover, supporting the recent ARPES findings.