The BCS-BEC crossover induced by a shallow band: Pushing standard   superconductivity types apart
  It is well-known that the appearance of almost-empty (shallow) conduction bands in solids strongly affects their superconducting properties. In a shallow band charge carriers are depleted and have nearly zero velocities so that the crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) is approached. Based on a two-band prototype system with one shallow and one deep band, we demonstrate that the fundamental phase diagram of the superconducting magnetic response changes qualitatively as compared to standard superconductors with only deep bands. The so-called intertype (IT) domain between superconductivity types I and II systematically expands in the phase diagram when passing from the BCS to BEC side: its width is inversely proportional to the squared Cooper-pair radius that shrinks several orders of magnitude through the crossover. We also show that the coupling to a stable condensate of the deep band makes the system rather robust against the otherwise strong superconducting fluctuations. Thus, the BCS-BEC crossover induced by a shallow band pushes standard superconductivity types wide apart so that the IT domain tends to dominate the phase diagram and therefore the magnetic properties of shallow-band superconductors. 
S. Wolf, A. Vagov, A. A. Shanenko, V. M. Axt, A. Perali, and J. Albino   Aguiar
cond-mat.supr-con