Effects of dynamical screening on the BCS-BEC crossover in double bilayer graphene: Density functional theory for exciton bilayers

We derive a gap equation for bilayer excitonic systems based on density functional theory and benchmark our results against quantum Monte-Carlo simulations and recent experiments on double bilayer graphene. The gap equation has a mean-field form but includes a consistent treatment of dynamical screening. We show that the gap survives at much higher densities than previously thought from mean-field estimates which gives strong indications that the double-bilayer graphene systems at zero magnetic field can be used as model systems to investigate the BCS-BEC crossover. Furthermore, we show that Josephson-like transfer of pairs can be substantial for small band gaps and densities.