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The efficient, large-scale generation and control of photonic modes guided by van der Waals materials remains as a challenge despite their potential for on-chip photonic circuitry. We report three-atom-thick waveguides—δ waveguides—based on wafer-scale molybdenum disulfide (MoS₂) monolayers that can guide visible and near-infrared light over millimeter-scale distances with low loss and an efficient in-coupling. The extreme thinness provides a light-trapping mechanism analogous to a δ-potential well in quantum mechanics and enables the guided waves that are essentially a plane wave freely propagating along the in-plane, but confined along the out-of-plane, direction of the waveguide. We further demonstrate key functionalities essential for two-dimensional photonics, including refraction, focusing, grating, interconnection, and intensity modulation, by integrating thin-film optical components with δ waveguides using microfabricated dielectric, metal, or patterned MoS₂. 

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 .