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Charge order pervades the phase diagrams of quantum materials where it competes with superconducting and magnetic phases, hosts electronic phase transitions and topological defects, and couples to the lattice generating intricate structural distortions. Incommensurate charge order is readily stabilized in manganese oxides, where it is associated with anomalous electronic and magnetic properties, but its nanoscale structural inhomogeneity complicates precise characterization and understanding of its relationship with competing phases. Leveraging atomic-resolution variable-temperature cryogenic scanning transmission electron microscopy, we characterize the thermal evolution of charge order as it transforms from its ground state in a model manganite system. We find that mobile networks of discommensurations and dislocations generate phase inhomogeneity and induce global incommensurability in an otherwise lattice-locked modulation. Driving the order to melt at high temperatures, the discommensuration density grows, and regions of order locally decouple from the lattice periodicity. Published by the American Physical Society2025 

Abstract Charge density waves are emergent quantum states that spontaneously reduce crystal symmetry, drive metal-insulator transitions, and precede superconductivity. In low-dimensions, distinct quantum states arise, however, thermal fluctuations and external disorder destroy long-range order. Here we stabilize ordered two-dimensional (2D) charge density waves through endotaxial synthesis of confined monolayers of 1T-TaS₂. Specifically, an ordered incommensurate charge density wave (oIC-CDW) is realized in 2D with dramatically enhanced amplitude and resistivity. By enhancing CDW order, the hexatic nature of charge density waves becomes observable. Upon heating via in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein topological defects form in the charge density wave. From these results, new regimes of the CDW phase diagram for 1T-TaS₂are derived and consistent with the predicted emergence of vestigial quantum order. 

We study the coupled charge density wave (CDW) and insulator-to-metal transitions in the 2D quantum material 1T-TaS₂. By applying in situ cryogenic 4D scanning transmission electron microscopy with in situ electrical resistance measurements, we directly visualize the CDW transition and establish that the transition is mediated by basal dislocations (stacking solitons). We find that dislocations can both nucleate and pin the transition and locally alter the transition temperatureT_cby nearly ~75 K. This finding was enabled by the application of unsupervised machine learning to cluster five-dimensional, terabyte scale datasets, which demonstrate a one-to-one correlation between resistance—a global property—and local CDW domain-dislocation dynamics, thereby linking the material microstructure to device properties. This work represents a major step toward defect-engineering of quantum materials, which will become increasingly important as we aim to utilize such materials in real devices. 

Abstract Mott metal–insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next‐generation energy‐efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in‐situ during a Mott transition in a Ca₂RuO₄thin film. Machine learning‐assisted X‐ray nanodiffraction together with cryogenic electron microscopy reveal multi‐scale periodic domain formation at and below the film transition temperature (T_Film ≈ 200–250 K) and a separate anisotropic spatial structure at and aboveT_Film. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties. 

Abstract The charge density wave material 1T-TaS₂exhibits a pulse-induced insulator-to-metal transition, which shows promise for next-generation electronics such as memristive memory and neuromorphic hardware. However, the rational design of TaS₂devices is hindered by a poor understanding of the switching mechanism, the pulse-induced phase, and the influence of material defects. Here, we operate a 2-terminal TaS₂device within a scanning transmission electron microscope at cryogenic temperature, and directly visualize the changing charge density wave structure with nanoscale spatial resolution and down to 300 μs temporal resolution. We show that the pulse-induced transition is driven by Joule heating, and that the pulse-induced state corresponds to the nearly commensurate and incommensurate charge density wave phases, depending on the applied voltage amplitude. With our in operando cryogenic electron microscopy experiments, we directly correlate the charge density wave structure with the device resistance, and show that dislocations significantly impact device performance. This work resolves fundamental questions of resistive switching in TaS₂devices, critical for engineering reliable and scalable TaS₂electronics.