Twisted bilayer graphene (TBG), particularly at the "magic angle" (θ ≈ 1.1°), exhibits fascinating correlated insulator behavior and superconductivity due to the formation of a flat band from the moiré pattern. The moiré structure, however, is not uniform spatially, influencing local electronic properties and leading to variations in charge transport measurements. Understanding the observed wide variations in phase diagrams and critical temperatures requires detailed knowledge of these local moiré variations. Existing experimental techniques have limitations in resolving these microscopic variations, including issues with capping layers, substrates, surface quality, and measurement speed. This research utilizes aberration-corrected low-energy electron microscopy (AC-LEEM) to overcome these limitations, offering large-scale, fast, and non-destructive imaging of TBG, including device-scale moiré images and dynamics on timescales of seconds. AC-LEEM also enables spectroscopic measurements by varying the landing energy of the electron beam, providing information about the material's unoccupied bands. The use of AC-LEEM avoids the need for suspended samples, allowing the imaging of samples with geometries similar to actual devices, including those with leads. While not demonstrated here, imaging through thin capping layers of hBN is also feasible. The study aims to provide a detailed characterization of the spatial and temporal variations of the moiré pattern in TBG, addressing the limitations of previous methods and furthering the understanding of the material's unique properties. This comprehensive study bridges the gap between macroscopic observations of TBG's unique behavior and its underlying microscopic structure and dynamics.

Previous research on twisted bilayer graphene (TBG) has highlighted the importance of the moiré superlattice in generating the unique electronic properties observed, including correlated insulator behavior and superconductivity at the magic angle. Studies have used various techniques such as scanning tunneling microscopy (STM), transmission electron microscopy (TEM), and transport measurements to probe the electronic structure and local properties of TBG. However, these techniques often face limitations in either spatial resolution, the ability to image through capping layers or in the ability to study dynamic behavior. Some studies have reported significant variations in the twist angle and strain across TBG samples, influencing the electronic properties. For example, the work by Uri et al. (Nature 2020) mapped the twist-angle disorder and Landau levels in magic-angle graphene, demonstrating the presence of significant local variations. Kazmierczak et al. (Nature Materials 2021) showed the presence of strain fields in TBG, highlighting the complexity of the system. The current study addresses these limitations by employing a new method based on aberration-corrected low-energy electron microscopy (AC-LEEM), providing higher spatial and temporal resolution, along with the ability to study device-like structures without the need for suspending the sample. This allows for more accurate mapping of the moiré structure and investigation of the dynamic behavior of the lattice.

The researchers fabricated TBG samples using the standard tear-and-stack method. Monolayer graphene was exfoliated onto a SiO2/Si substrate, and a polycarbonate (PC)/polydimethylsiloxane (PDMS) stamp was used for transfer and rotation of one graphene layer by a specific angle before stacking. The TBG was then transferred onto an hBN flake on a silicon substrate, and the PC layer was dissolved. All LEEM measurements were performed using the ESCHER LEEM instrument. Samples were heated to 500 °C to remove any residue and minimize hydrocarbon contamination. Imaging was performed at elevated temperatures (450-500 °C unless specified otherwise). LEEM spectra were obtained to determine the local graphene layer count. To visualize the graphene layer count, a false-color image was created by combining stitched overviews at different characteristic energies (4 eV, 8 eV, and 17 eV). Imaging at higher energies (37 eV) provided optimal contrast for visualizing the moiré lattice. To analyze moiré lattice distortions, the researchers used adaptive geometric phase analysis (GPA). This method involved multiplying the original image with complex reference waves followed by low-pass filtering to obtain GPA phase differences which were converted to the displacement field. The displacement field fully describes the distortion of the moiré lattice, allowing extraction of parameters such as local twist angle and heterostrain. To study the dynamics of the moiré lattice, time series of images were taken at 500 °C, capturing the movement of domain boundaries. GPA was used to quantify these fluctuations. For stitching high resolution images across a large field of view, the sample was scanned and custom stitching software was developed, using a log-polar transformation-based method to compensate for minor variations. In addition, the ab initio Bloch-wave-based scattering method was used to calculate the theoretical reflectivity spectra.

This study using AC-LEEM revealed several key findings regarding the moiré structure and dynamics in TBG: 1. **Smaller Spatial Variation:** The spatial variation in twist angle within individual moiré domains was found to be significantly smaller (by a factor of 3-10) than previously reported. Standard deviations ranged from 0.005° to 0.015° within domains, highlighting the improved accuracy of the AC-LEEM technique. 2. **Thermal Fluctuations:** Thermal fluctuations of the moiré lattice were observed at 500 °C, corresponding to collective atomic displacements of less than 70 pm on a timescale of seconds. These fluctuations involve the collective movement of millions of atoms, but over very small distances (less than half the width of a domain boundary). This is evident in the movement of domain boundaries on the order of 4nm. 3. **No Untwisting at High Temperatures:** No untwisting of the graphene layers was observed even at temperatures as high as 600 °C, contrary to previous concerns. This suggests that high-temperature annealing can be used to reduce local disorder and improve TBG quality. 4. **Edge Dislocations:** Individual edge dislocations in the atomic and moiré lattices were observed. These topological defects are magnified by the moiré structure and are anticipated to exhibit unique local electronic properties. These dislocations were stable even at elevated temperatures and under prolonged low-energy electron irradiation. 5. **Moiré Magnification:** The moiré pattern acts as a magnifying glass, enabling the detection of sub-angstrom changes in the atomic lattice in real time. 6. **Quantification of Distortion:** Geometric phase analysis (GPA) was successfully extended to allow detailed quantitative analysis of moiré lattice distortions, including extraction of local twist angle and heterostrain. Strain observed was around a few tenths of a percent, considered significant enough to potentially induce a quantum phase transition. The observed strain variations within domains were significantly lower than in previous studies. The researchers suggest that high-temperature annealing reduces lattice disorder by allowing the system to reach a more homogeneous, lower-energy state. The observed thermal fluctuations at 500 °C could be a source of the short-range twist angle disorder observed in lower-temperature experiments.

The findings of this study significantly advance the understanding of the moiré structure and dynamics in TBG. The observed smaller spatial variation in twist angle within domains than previously reported suggests that previous studies might have overestimated the disorder. The observation of thermal fluctuations, however, highlights a dynamic aspect of the moiré lattice that has not been fully explored. The lack of untwisting at high temperatures is encouraging for the fabrication of high-quality TBG devices. The discovery of edge dislocations opens up new avenues for exploring their influence on the local electronic properties. The use of AC-LEEM has provided high-quality data, surpassing the limitations of previously used methods. The combination of high-temperature annealing and the use of AC-LEEM provide insights into minimizing local disorder in TBG and hence optimizing device fabrication. The study suggests that frozen-in thermal fluctuations may contribute significantly to the observed twist angle disorder. Future studies employing combined techniques like AC-LEEM with techniques such as STS, nanoARPES, or in situ potentiometry are suggested for a more thorough investigation of electronic properties near the dislocations. The results highlight the importance of considering both static and dynamic aspects of the moiré lattice when studying TBG and its fascinating properties.

This study provides a comprehensive analysis of moiré deformation and dynamics in TBG using AC-LEEM. Key findings include smaller spatial variation than previously reported, the observation of thermal fluctuations without untwisting at high temperatures, and the identification of stable edge dislocations. This work demonstrates the power of AC-LEEM for studying TBG and suggests that high-temperature annealing can reduce local disorder. Future studies should focus on the detailed statistics of domain boundary dynamics versus temperature, and on combining AC-LEEM with other techniques to investigate the electronic properties of edge dislocations.

While the AC-LEEM technique offers significant advantages, there are limitations to consider. The point spread function (PSF) of the GPA analysis introduces a broadening effect, potentially underestimating the variation at small scales. Also, the study mainly focuses on TBG samples produced by a specific method. Extending the findings to other sample fabrication methods would further solidify the conclusions. Furthermore, while the study shows no untwisting up to 600 °C, a direct comparison to theoretical predictions, and investigation of larger area TBG is warranted to fully differentiate between local pinning and intrinsic rotational stability. Finally, the study's focus on relatively small areas, even with stitching, might not be completely representative of larger TBG samples.