Theory of BCS-to-BEC Crossover in FeSe

The BCS-BEC crossover has been challenging to realize in condensed matter systems. Recently, there has been experimental evidence for such a transition in a FeSe monolayer on a trilayer graphene substrate. There are two crucial ingredients in this observation: 1) Pairing interactions induced by spin fluctuations can condense Cooper pairs even in incipient bands. 2) The Fermi level of the FeSe monolayer is controlled by the local work function of the substrate which depends on how the graphene layers are stacked. At the interface between ABA and ABC stacked graphene, the chemical potential in the FeSe monolayer crosses the hole band edge, such that the hole carriers in the FeSe monolayer are in a BCS state on one side and in a BEC state on the other. In this talk, I will describe a minimal two-band model that explains these observations and discuss how the parameters of the model must be chosen to make contact with the real world. Furthermore, I will treat the problem using a real-space Bogoliubov-de Gennes approach to also explain interface effects.