Fractal photonic topological insulators

Topological insulators constitute a newly characterized state of matter that contains scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, because the invariants that describe the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals composed exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared with the corresponding honeycomb lattice. By going beyond the confines of the bulk- boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

Automated summary

Conventional wisdom suggests that the insulating bulk is crucial for defining the topological properties of topological insulators. However, our study shows that even without an insulating bulk, fractal topological insulators composed exclusively of edge sites can still support topologically protected edge states. Additionally, we find that light transport in our topological fractal system exhibits higher velocities compared to the corresponding honeycomb lattice.