Scalable van der Waals epitaxy of tunable moir\'e heterostructures

The unique physics found in moir\'e superlattices of twisted or lattice-mismatched atomic layers hold great promise for future quantum technologies. However, twisted configurations are typically thermodynamically unfavorable, making the accurate twist angle control in direct growth implausible. While rotationally aligned moir\'e superlattices based on lattice-mismatched layers such as WSe2/WS2 can be synthesized, they lack the critical tunability of the moir\'e period and the moir\'e formation mechanisms are not well-understood. Here, we report the scalable, thermodynamically driven van der Waals epitaxy of stable moir\'es with tunable period from 10 to 45 nanometers, based on lattice mismatch engineering in two WSSe layers with adjustable chalcogens ratios. Contrarily to conventional epitaxy, where lattice mismatch induced stress hinders high-quality growth, we reveal the key role of bulk stress in moir\'e formation, as well as its unique interplay with edge stress in shaping the moir\'e growth modes. Moreover, the synthesized superlattices display tunable interlayer, and moir\'e intralayer excitons. Our studies unveil the unique epitaxial science of moir\'e synthesis and lay the foundations for moir\'e-based technologies.