Abstract
The appearance of a shallow band(s) drives a superconductor towards the BCS-BEC crossover, conventionally associated with notable changes in single-particle properties and an elevated critical temperature. Here we demonstrate that the proximity to the crossover induced by a shallow band has also a dramatic effect on the phase diagram of the superconducting magnetic properties. When the system passes from the BCS to BEC regime, the intertype domain between superconductivity types I and II enlarges systematically, being inversely proportional to the square of the Cooper-pair radius, the main parameter that controls the BCS-BEC superconductivity. We also show that despite the presence of a shallow band, the condensate fluctuations are suppressed when it coexists in one material with standard deep bands, as in recent iron chalcogenides ${\mathrm{Fe}\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ and $\mathrm{FeSe}$.
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