  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 band 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-Tc superconductivity. The
ratio between the gap and the Fermi energy in a given band results to be 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.
