Twisted bilayer graphene (TBG) displays a host of correlated electronic phases associated with the formation of flat electronic bands near an interlayer 'magic angle' (MA) of 1.1 degrees 1-9 . Intralayer lattice reconstruction 10-13 , which involves local rotations with consequent localized strain 14,15 , and symmetry breaking due to extrinsic heterostrain have significant implications for electronic behavior at the MA 9,16,17 . Although reconstruction and strain are therefore fundamental to the properties of TBG, directly mapping the reconstruction mechanics in the MA regime has been elusive and the strain tensor fields of TBG have not been measured. Here, we introduce Bragg interferometry, based on four-dimensional scanning transmission electron microscopy (4D-STEM) 18-21 , to capture the atomic displacement fields of TBG with twist angles ranging from 0.1 to 1.6 degrees. Sub-nanometer resolution allows us to image atomic reconstruction in MA-TBG and resolve twist angle disorder at the level of individual moiré domains. We quantitatively map the strain tensor fields and uncover that reconstruction proceeds in two distinct regimes depending on the twist angle-in contrast to previous models depicting a single continuous process-and we distinguish the contributions of these regimes to the band structure. Further, we find that over a twist angle range encompassing the MA, applied heterostrain accumulates anisotropically in saddle point (SP) regions to generate distinctive striped strain phases. Our results thus establish the reconstruction mechanics underpinning the twist angle dependent electronic behavior of TBG, and provide a new framework for directly visualizing strain and reconstruction in other moiré materials.

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Two-dimensional (2D) magnetic crystals hold promise for miniaturized and ultralow power electronic devices that exploit spin manipulation. In these materials, large, controllable magnetocrystalline anisotropy (MCA) is a prerequisite for the stabilization and manipulation of long-range magnetic order. In known 2D magnetic crystals, relatively weak MCA typically results in soft ferromagnetism. Here, we demonstrate that ferromagnetic order persists down to the thinnest limit of Fe x TaS 2 (Fe-intercalated bilayer 2H-TaS 2 ) with giant coercivities up to 3 T. We prepare Fe-intercalated TaS 2 by chemical intercalation of van der Waalslayered 2H-TaS 2 crystals and perform variable-temperature transport, transmission electron microscopy, and confocal Raman spectroscopy measurements to shed new light on the coupled effects of dimensionality, degree of intercalation, and intercalant order/disorder on the hard ferromagnetic behavior of Fe x TaS 2 . More generally, we show that chemical intercalation gives access to a rich synthetic parameter space for low-dimensional magnets, in which magnetic properties can be tailored by the choice of the host material and intercalant identity/amount, in addition to the manifold distinctive degrees of freedom available in atomically thin, van der Waals crystals.

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 MoS2 and WSe2/MoS2 heterobilayers. 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.

Optical polarizers encompass a class of anisotropic materials that pass-through discrete orientations of light and are found in wide-ranging technologies, from windows and glasses to cameras, digital displays and photonic devices. The wire-grids, ordered surfaces, and aligned nanomaterials used to make polarized films cannot be easily reconfigured once aligned, limiting their use to stationary cross-polarizers in, for example, liquid crystal displays. Here we describe a supramolecular material set and patterning approach where the polarization angle in stand-alone films can be precisely defined at the single pixel level and reconfigured following initial alignment. This capability enables new routes for non-binary information storage, retrieval, and intrinsic encryption, and it suggests future technologies such as photonic chips that can be reconfigured using non-contact patterning.