Eliashberg Theory for Dynamical Screening in Bilayer Exciton Condensation

We study the effect of dynamical screening of interactions on the transition temperatures (Tc) of exciton condensation in a symmetric bilayer of quadratically dispersing electrons and holes by solving the linearized Eliashberg equations for the anomalous interlayer Green's functions. We find that Tc is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. Tc is suppressed well below that predicted by a Hartree Fock mean field theory with unscreened Coulomb interaction, but is above the estimates from the statically screened Coulomb interaction. Furthermore, using a diagrammatic framework, we show that the system is always an exciton condensate at zero temperature but Tc is exponentially small for large interlayer separation.