  The nonequilibrium excitonic insulator (NEQ-EI) is an excited state of matter
characterized by a finite density of coherent excitons and a time-dependent
macroscopic polarization. The stability of this exciton superfluid as the
density grows is jeopardized by the increased screening efficiency of the
looser excitons. In this work we put forward a Hartree plus Screened Exchange
HSEX scheme to predict the critical density at which the transition toward a
free electron-hole plasma occurs. The dielectric function is calculated
self-consistently using the NEQ-EI polarization and found to vanish in the
long-wavelength limit. This property makes the exciton superfluid stable up to
relatively high densities. Numerical results for the MoS$_{2}$ monolayers
indicate that the NEQ-EI phase survives up to densities of the order of
$10^{12}\mathrm{cm}^{-2}$.
