  Recent pump-probe experiments demonstrate the possibility that Dirac
materials may be driven into transient excited states describable by two
chemical potentials, one for the electrons and one for the holes. Given the
Dirac nature of the spectrum, such an inverted population allows the optical
tunability of the density of states of the electrons and holes, effectively
offering control of the strength of the Coulomb interaction. Here we discuss
the feasibility of realizing transient excitonic instabilities in
optically-pumped Dirac materials. We demonstrate, theoretically, the reduction
of the critical coupling leading to the formation of a transient condensate of
electron-hole pairs and identify signatures of this state. Furthermore, we
provide guidelines for experiments by both identifying the regimes in which
such exotic many-body states are more likely to be observed and estimating the
magnitude of the excitonic gap for a few important examples of existing Dirac
materials. We find a set of material parameters for which our theory predicts
large gaps and high critical temperatures and which could be realized in future
Dirac materials. We also comment on transient excitonic instabilities in
three-dimensional Dirac and Weyl semimetals. This study provides the first
example of a transient collective instability in driven Dirac materials.
