Science: Fractal photonic topological insulators

TOBIAS BIESENTHAL, LUKAS J. MACZEWSKY, ZHАOJU YANG, MARK KREMER, MORDECHAI SEGEV, 

ALEXANDER SZAMEIT, AND MATTHIAS HEINRICH 

Topological insulators constitute a novel state of matter with scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, since the invariants describing the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals comprised 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 to 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.

SCIENCE, 2022, DOI: 10.1126/SCIENCE.ABM2842

The published article is available at https://www.science.org/doi/10.1126/science.abm2842