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.
Highlights
In a recent experiment [1] on two bilayer graphene sheets separated by a WSe2 insulating barrier an enhanced tunneling rate was measured, which indicates the formation of an exciton condensate
The method is applied to double bilayer graphene, which is the most promising bilayer candidate for achieving exciton condensation without an applied magnetic field
We begin by giving a brief account of the derivation, we benchmark our method against quantum Monte Carlo (QMC) simulations for simplified models [14], and consider realistic systems where we compare to the experimental results in Ref. [1] and mean-field calculations in Ref. [10]
Summary
In a recent experiment [1] on two bilayer graphene sheets separated by a WSe2 insulating barrier an enhanced tunneling rate was measured, which indicates the formation of an exciton condensate. Contrary to mean-field theories, the results from our effective gap equation qualitatively agree both with QMC simulations and experimental measurements. It is straightforward to show that a static exchange approximation to the self-energy yields the usual mean-field gap equation, kγ
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