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High-temperature polaronic lattice distortions and charge ordering through the charge-density wave and quantum spin liquid phase transitions in 1T-TaS$_{2}$

Interesting emergent behavior in quantum materials arises when the interaction of electrons with the lattice leads to partial localization and ordering of charge at low temperatures. The triangular lattice of some transition metal dichalcogenides additionally presents an interesting case, where spin order is frustrated, leading to an additional complex interplay of interactions involving spin, charge and lattice degrees of freedom. Here we present a study of local symmetry breaking of the lattice structure in the layered dichalcogenide material 1T-TaS$_{2}$ using x-ray pair-distribution function measurements. Remarkably, we observe symmetry-breaking polaronic distortions of the lattice structure around individual localized electrons at temperatures well above any of the known long-range ordered phases. These characteristic polaronic signatures remain on cooling through the spin and charge ordered states, eventually revealing a new transition near 50 K to a state displaying partially restored symmetry and significant inter-layer dimerization. The order parameter associated with the observed local atomic displacements and symmetry-allowed polaron spin structure in the ground state suggests that charge ordering is driven by the crystallization of polarons, rather than conventional Fermi surface nesting. Symmetry analysis shows that the distorted structure is consistent with a breakup of the QSL phase at low temperature, concurrent with the disappearance of domains in the charge order.