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The concept of remote epitaxy involves a two-dimensional van der Waals layer covering the substrate surface, which still enable adatoms to follow the atomic motif of the underlying substrate. The mode of growth must be carefully defined as defects, e.g., pinholes, in two-dimensional materials can allow direct epitaxy from the substrate, which, in combination with lateral epitaxial overgrowth, could also form an epilayer. Here, we show several unique cases that can only be observed for remote epitaxy, distinguishable from other two-dimensional material-based epitaxy mechanisms. We first grow BaTiO₃on patterned graphene to establish a condition for minimizing epitaxial lateral overgrowth. By observing entire nanometer-scale nuclei grown aligned to the substrate on pinhole-free graphene confirmed by high-resolution scanning transmission electron microscopy, we visually confirm that remote epitaxy is operative at the atomic scale. Macroscopically, we also show variations in the density of GaN microcrystal arrays that depend on the ionicity of substrates and the number of graphene layers. 

Although flakes of two-dimensional (2D) heterostructures at the micrometer scale can be formed with adhesive-tape exfoliation methods, isolation of 2D flakes into monolayers is extremely time consuming because it is a trial-and-error process. Controlling the number of 2D layers through direct growth also presents difficulty because of the high nucleation barrier on 2D materials. We demonstrate a layer-resolved 2D material splitting technique that permits high-throughput production of multiple monolayers of wafer-scale (5-centimeter diameter) 2D materials by splitting single stacks of thick 2D materials grown on a single wafer. Wafer-scale uniformity of hexagonal boron nitride, tungsten disulfide, tungsten diselenide, molybdenum disulfide, and molybdenum diselenide monolayers was verified by photoluminescence response and by substantial retention of electronic conductivity. We fabricated wafer-scale van der Waals heterostructures, including field-effect transistors, with single-atom thickness resolution.