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Abstract Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moiré superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moirés has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS₂and WSe₂/MoS₂heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moiré layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moiré potential. 

Bragg interferometry (BI) is an imaging technique based on four-dimensional scanning transmission electron microscopy (4D-STEM) wherein the intensities of select overlapping Bragg disks are fit or more qualitatively analyzed in the context of simple trigonometric equations to determine local stacking order. In 4D-STEM based approaches, the collection of full diffraction patterns at each real-space position of the scanning probe allows the use of precise virtual apertures much smaller and more variable in shape than those used in conventional dark field imaging such that even buried interfaces marginally twisted from other layers can be targeted. With a coarse-grained form of dark field ptychography, BI uses simple physically derived fitting functions to extract the average structure within the illumination region and is, therefore, viable over large fields of view. BI has shown a particular advantage for selectively investigating the interlayer stacking and associated moiré reconstruction of bilayer interfaces within complex multi-layered structures. This has enabled investigation of reconstruction and substrate effects in bilayers through encapsulating hexagonal boron nitride and of select bilayer interfaces within trilayer stacks. However, the technique can be improved to provide a greater spatial resolution and probe a wider range of twisted structures, for which current limitations on acquisition parameters can lead to large illumination regions and the computationally involved post-processing can fail. Here, we analyze these limitations and the computational processing in greater depth, presenting a few methods for improvement over previous works, discussing potential areas for further expansion, and illustrating the current capabilities of this approach for extracting moiré-scale strain. 

In conventional ferroelectric materials, polarization is an intrinsic property limited by bulk crystallographic structure and symmetry. Recently, it has been demonstrated that polar order can also be accessed using inherently non-polar van der Waals materials through layer-by-layer assembly into heterostructures, wherein interfacial interactions can generate spontaneous, switchable polarization. Here, we show that deliberate interlayer rotations in multilayer vdW heterostructures modulate both the spatial ordering and switching dy- namics of polar domains. The engendered tunability is unparalleled in conventional bulk ferroelectrics or polar bilayers. By means of operando transmission electron microscopy we show how alterations of the relative rotations of three WSe2 layers produce structural poly- types with distinct arrangements of polar domains with either a global or localized switching response. Furthermore, the presence of uniaxial strain generates structural anisotropy that yields a range of switching behaviors, coercivities, and even tunable biased responses. We also provide evidence of mechanical coupling between the two interfaces of the trilayer, a key consideration for the control of switching dynamics in polar multilayer structures more broadly. 

Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously.