Phonon-induced pseudogap phase in TiSe$_2$
To comprehend quantum ordered states, such as charge density waves (CDW), in layered transition metal dichalcogenides (TMDCs), it is essential to uncover their underlying normal states. Here, we use time- and angle-resolved extreme ultraviolet photoemission spectroscopy and ab initio electron-phonon calculations to perform excited state band mapping of three prototypical 1T TMDCs, i.e., TiSe$_2$, HfTe$_2$, and ZrTe$_2$, at room temperature. The results reveal the profound impact of strong electron-phonon-induced thermal fluctuations on the normal-phase electronic structure. Specifically, in the moderate electron-phonon coupling regime, as in HfTe$_2$ and ZrTe$_2$, thermal fluctuations only lead to small spectral broadening and band renormalization. In the strongly coupled case, exemplified by TiSe$_2$, we observe soft-phonon-induced, momentum-dependent suppression of spectral weight, i.e., pseudogaps - extending up to 1 eV above the Fermi level. Our work establishes the normal phase of TiSe$_2$ as a phonon-induced pseudogap phase governed by strong CDW fluctuations, thereby uncovering previously missing aspects of the TiSe$_2$ phase diagram, with broader implications for other TMDCs in the strong electron-phonon coupling regime.