Uncovering the nature of transient and metastable non-equilibrium phases in 1$T$-TaS$_2

Complex systems are characterized by strong coupling between different microscopic degrees of freedom. Photoexcitation of such materials can drive them into new transient and long-lived hidden phases that may not have any counterparts in equilibrium. By exploiting femtosecond time- and angle-resolved photoemission spectroscopy, we probe the photoinduced transient phase and the recovery dynamics of the ground state in a complex material: the charge density wave (CDW)-Mott insulator 1$T$-TaS$_2$. We reveal striking similarities between the band structures of the transient phase and the (equilibrium) structurally undistorted metallic phase, with evidence for the coexistence of the low-temperature Mott insulating phase and high-temperature metallic phase. Following the transient phase, we find that the restoration of the Mott and CDW order begins around the same time. This highlights that the Mott transition is tied to the CDW structural distortion, although earlier studies have shown that the collapse of Mott and CDW phases are decoupled from each other. Interestingly, as the suppressed order starts to recover, a long-lived metastable phase emerges before the material recovers to the ground state. Our results demonstrate that it is the CDW lattice order that drives the material into this metastable phase, which is indeed a commensurate CDW-Mott insulating phase but with a smaller CDW amplitude. Moreover, we find that the long-lived state emerges only under strong photoexcitation and has no evidence when the photoexcitation strength is weak.