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We study the effect of dynamical screening of interactions on the transitiontemperatures ($T_c$) of exciton condensation in a symmetric bilayer ofquadratically dispersing electrons and holes by solving the linearizedEliashberg equations for the anomalous interlayer Green's functions. We findthat $T_c$ is finite for the range of density and layer separations studied,decaying exponentially with interlayer separation. $T_c$ is suppressed wellbelow that predicted by a Hartree Fock mean field theory with unscreenedCoulomb interaction, but is above the estimates from the statically screenedCoulomb interaction. Furthermore, using a diagramatic framework, we show thatthe system is always an exciton condensate at zero temperature but $T_c$ isexponentially small for large interlayer separation.

Eliashberg theory for bilayer exciton condensation