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.
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