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Driven and non-equilibrium quantum states of matter have attracted growinginterest in both theoretical and experimental studies in condensed matterphysics. We review recent progress in realizing transient collective states indriven or pumped Dirac materials (DMs). In particular, we focus onoptically-pumped DMs which have been theoretically proposed as a promisingplatform for observation of a transient excitonic instability.  Optical pumping combined with the linear (Dirac) dispersion of the electronicspectrum offers a knob for tuning the effective interaction between thephotoexcited electrons and holes, and thus provides a way of reducing thecritical coupling for excitonic instability. As a result, a transient excitoniccondensate could be achieved in a pumped DM while it is not feasible inequilibrium. We provide a unifying theoretical framework for describingtransient collective states in two- and three-dimensional DMs. We describeexperimental signatures of the transient excitonic state and summarizenumerical estimates of the magnitude of the effect, namely the size of thedynamically-induced excitonic gaps and the values of the critical temperaturesfor several specific systems. We also discuss general guidelines foridentifying promising material candidates.Finally, we comment recentexperimental efforts in realizing transient excitonic condensate in pumped DMsand outline outstanding issues and possible future directions.

Transient excitonic states in optically-pumped Dirac materials: overview of recent work