BCS–BEC crossover in multi-band systems with a boson–fermion coupling at zero temperature

• Superconductivity depends of the threshold energy for forming a tightly bound pair.
• Increasing the strength of hybridization superconductivity is lowered.
• The crossover is driven by increasing the inter-site interaction and the boson–fermion coupling strength.
• The crossover can be driven by changing the threshold energy of bosons.

We study the crossover between the BCS (Bardeen, Cooper, Schrieffer) and BEC (Bose–Einstein Condensate) superfluid states in a multi-band boson–fermion model at zero temperature. We consider an attractive interaction between different fermion states and a hybridization between them. The bosons are composed of tightly bound fermion pairs that coexist and interact with the single fermions, via an isotropic boson–fermion coupling g. At zero temperature, where all bosons are condensed, the model has a superconducting phase characterized by a finite composite   order parameter, Δ̃ab=Δab-gϕ, where ΔabΔab and ϕ   are the BCS and BEC order parameters, respectively. The zero temperature phase diagram in terms of ΔabΔab and ϕ is obtained as function of the attractive inter-site interaction, the hybridization, the boson–fermion coupling and the threshold energy for forming a pair of tightly bound fermions. We also discuss the zero temperature BCS–BEC crossover driven by changing the attractive interaction, the boson–fermion coupling strength, and the threshold energy. Our results should be relevant for high temperature superconductors and cold atom systems.