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We demonstrate the rise-and-fall of multiple pseudogaps in theBardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover intwo-band fermionic systems having different pairing strengths in the deep bandand in the shallow band. The striking features of this phenomenon are anunusual many-body screening of pseudogap state and the importance ofpair-exchange couplings, which induces multiple pseudogap formation in the twobands. The multi-band configuration suppresses pairing fluctuations and thepseudogap opening in the strongly-interacting shallow band at smallpair-exchange couplings by screening effects, with possible connection to thepseudogap phenomenology in iron based superconductors. On the other hand, themultiple pseudogap mechanism accompanies with the emergence of binary preformedCooper pairs originating from interplay between intra-band and pair-exchangecouplings.

Mechanism of screening or enhancing the pseudogap throughout the two-band Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover