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Abstract Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 . 

The large-scale synthesis of high-quality thin films with extensive tunability derived from molecular building blocks will advance the development of artificial solids with designed functionalities. We report the synthesis of two-dimensional (2D) porphyrin polymer films with wafer-scale homogeneity in the ultimate limit of monolayer thickness by growing films at a sharp pentane/water interface, which allows the fabrication of their hybrid superlattices. Laminar assembly polymerization of porphyrin monomers could form monolayers of metal-organic frameworks with Cu 2+ linkers or covalent organic frameworks with terephthalaldehyde linkers. Both the lattice structures and optical properties of these 2D films were directly controlled by the molecular monomers and polymerization chemistries. The 2D polymers were used to fabricate arrays of hybrid superlattices with molybdenum disulfide that could be used in electrical capacitors.