We demonstrate the rise and fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of the pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multiband configuration suppresses pairing fluctuations and the pseudogap opening in the strongly interacting shallow band at small pair-exchange couplings by screening effects, with a possible connection to the pseudogap phenomenology in iron-based superconductors. On the other hand, the multiple pseudogap mechanism is accompanied by the emergence of binary preformed Cooper pairs originating from the interplay between intraband and pair-exchange couplings.

• Received 9 September 2020
• Revised 3 November 2020
• Accepted 19 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.220504