Competing orders in an extended Falicov-Kimball model

We study the interplay between superconducting pairing, exciton and charge-density wave in a correlated electron model, the Falicov-Kimball model, extended by a hybridization term between spinless fermions and also by an attractive pairing in the particle channel. A self-consistent Hartree-Fock BdG mean-field calculation shows that the hybridization V and Coulomb repulsion U favour in binding an exciton but both are detrimental to the formation of superconducting pairing, whereas, CDW is favoured by Coulomb interaction and disfavoured by V . There is a coexistence regime for superconductivity, CDW and excitonic order in the parameter space