The effect of screening on excitonic condensation in double-layer graphene

A double-layer graphene system - where two layers of graphene are embedded in a dielectric and are separated by a distance d - is expected to support ground states with interlayer coherence. In particular, when one layer has electrons as carriers and the other has holes, the system supports a uniform excitonic condensate ground state. We investigate the effect of screened electron-electron interaction on the formation and the strength of excitonic condensation using complementary momentum-space and real-space mean-field analyses. We obtain the dependence of the excitonic order parameter $\Delta_k$, quasiparticle energy dispersion $E_k$, and the quasiparticle density-of-states on the screening-length and the interlayer distance. By focusing on the momentum-dependence of the excitonic order parameter $\Delta_k$, we point out the differences between our results and those obtained in the literature.