  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.
