  Driven and non-equilibrium quantum states of matter have attracted growing
interest in both theoretical and experimental studies in condensed matter
physics. We review recent progress in realizing transient collective states in
driven or pumped Dirac materials (DMs). In particular, we focus on
optically-pumped DMs which have been theoretically proposed as a promising
platform for observation of a transient excitonic instability.
  Optical pumping combined with the linear (Dirac) dispersion of the electronic
spectrum offers a knob for tuning the effective interaction between the
photoexcited electrons and holes, and thus provides a way of reducing the
critical coupling for excitonic instability. As a result, a transient excitonic
condensate could be achieved in a pumped DM while it is not feasible in
equilibrium. We provide a unifying theoretical framework for describing
transient collective states in two- and three-dimensional DMs. We describe
experimental signatures of the transient excitonic state and summarize
numerical estimates of the magnitude of the effect, namely the size of the
dynamically-induced excitonic gaps and the values of the critical temperatures
for several specific systems. We also discuss general guidelines for
identifying promising material candidates.Finally, we comment recent
experimental efforts in realizing transient excitonic condensate in pumped DMs
and outline outstanding issues and possible future directions.
