When superconductivity crosses over: From BCS to BEC

New developments in superconductivity, particularly through unexpected and often surprising forms of superconducting materials, continue to excite the community and stimulate theory. It is now becoming clear that there are two distinct platforms for superconductivity: natural and synthetic materials. The study of these artificial materials has greatly expanded in the past decade or so, with the discoveries of new forms of superfluidity in artificial heterostructures and the exploitation of proximitization. Natural superconductors continue to surprise through Fe-based pnictides and chalcogenides, and nickelates as well as others. This review presents a two-pronged investigation into such superconductors, with an emphasis on those that have come to be understood to belong somewhere between the Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) regimes. The nature of this “crossover” superconductivity, which is to be distinguished from crossover superfluidity in atomic Fermi gases, is a focus here. Multiple ways of promoting a system out of the BCS and into the BCS-BEC crossover regime are addressed in the context of concrete experimental realizations. These involve natural materials, such as organic conductors, as well as artificial, mostly two-dimensional materials, such as magic-angle twisted bilayer and trilayer graphene, or gate-controlled devices, as well as one-layer and interfacial superconducting films. Such developments should be viewed as a celebration of BCS theory, as it is now clear that, even though this theory was initially implemented with the special case of weak correlations in mind, it can be extended in a natural way to treat the case of these more exotic strongly correlated superconductors.