Abstract Topological transitions are fundamental phenomena in electronics, photonics, and quantum technologies. However, their scalability and tunability are constrained by material properties or structural rigidities. Here, we demonstrate that plasmonic Moiré superlattices offer a platform for programmable, large-range topological transitions via wavefront engineering. By tailoring the phases of elementary evanescent waves in hexagonal systems, we create Moiré lattices of optical skyrmions, whose topological invariants evolution is programmable and scalable. Theoretical calculations indicate that the topological invariants span a range of values going from −58 to +58, extendable by tuning the Moiré angle. Remarkably, these values are constrained by symmetry to exclude integer multiples of 3/2, revealing an intrinsic link between symmetry and topological quantization. Our work establishes a versatile control platform of real-space topology for exploring topological transitions mechanisms and studying critical topological phenomena, further promoting breakthroughs in structured light, photonic computing, and condensed matter physics.
Tian et al. (Thu,) studied this question.