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Emergence of a hidden-order phase well below the charge density wave transition in a topological Weyl semimetal (TaSe$_4$)$_2$I

The emergence of a charge density wave (CDW) in a Weyl semimetal -- a correlated topological phase, is exceptionally rare in condensed matter systems. In this context, the quasi-one-dimensional type-III Weyl semimetal (TaSe$_4$)$_2$I undergoes a CDW transition at $T_{\mathrm{CDW}} \approx 263$~K, providing an exceptional platform to investigate correlated topological CDW states. Here, we uncover an additional hidden-order phase transition at $T^* \sim 100$ K, well below the CDW onset, using low-frequency resistance noise spectroscopy, electrical transport, and thermoelectric measurements. This transition is characterized by a sharp enhancement in the noise exponent ($α$) and variance of resistance fluctuations. Analysis of higher-order statistics of resistance fluctuations reveals the correlated dynamics underlying the transition. A pronounced anomaly in the Seebeck coefficient near $T^*$ further suggests a Fermi surface reconstruction. First-principles calculations reveal a structural distortion from the high-symmetry $I422$ phase to a low-symmetry $C2$ phase, via an intermediate $I4$ symmetry. This leads to renormalization of the electronic structure near the Fermi level and opening of a bandgap in the hidden-order phase. These findings demonstrate a previously unidentified correlated phase transition in the topological CDW-Weyl semimetal (TaSe$_4$)$_2$I, enriching the phase diagram of this material and establishing it as an ideal platform for studying intertwined electronic and structural orders.