# Scalable and programmable topological transitions in plasmonic Moiré superlattices

## TL;DR

Researchers show that plasmonic Moiré superlattices enable scalable and tunable topological transitions, offering a new platform for studying topological phenomena in physics.

## Contribution

The work introduces a programmable platform for large-range topological transitions using plasmonic Moiré superlattices and reveals a symmetry-based selection rule for topological invariants.

## Key findings

- Topological invariants in the system range from -58 to +58 and can be extended by adjusting the Moiré angle.
- Symmetry constraints exclude integer multiples of 3/2 from the topological invariants, linking symmetry to quantization.
- The platform enables real-space topological control for applications in photonic computing and condensed matter physics.

## 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.

Material properties and structural rigidity make topological transitions hard to scale and program. Here, authors use moiré superlattices of optical skyrmions to achieve broad tuneability of topological transitions and revealing a symmetry-related selection rule for the system topological invariants, excluding integer multiples of 3/2.