Eliashberg Theory for Dynamical Screening in Bilayer Exciton Condensation

We study the effect of dynamical screening of interactions on the transition temperatures (T_{c}) 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 T_{c} is finite for the range of density and layer separations studied, decaying exponentially with interlayer separation. T_{c} 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 T_{c} is exponentially small for large interlayer separation.