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

Abstract

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.