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Charge density waves are emergent quantum states that spontaneously reducecrystal symmetry, drive metal-insulator transitions, and precedesuperconductivity. In low-dimensions, distinct quantum states arise, however,thermal fluctuations and external disorder destroy long-range order. Here westabilize ordered two-dimensional (2D) charge density waves through endotaxialsynthesis of confined monolayers of 1T-TaS$_2$. Specifically, an orderedincommensurate charge density wave (oIC-CDW) is realized in 2D withdramatically enhanced amplitude and resistivity. By enhancing CDW order, thehexatic nature of charge density waves becomes observable. Upon heating viain-situ TEM, the CDW continuously melts in a reversible hexatic process whereintopological defects form in the charge density wave. From these results, newregimes of the CDW phase diagram for 1T-TaS$_2$ are derived and consistent withthe predicted emergence of vestigial quantum order.

Endotaxial Stabilization of 2D Charge Density Waves with Long-range Order