Photonic Floquet topological insulators in a fractal lattice

TL;DR

This paper introduces photonic Floquet topological insulators in a fractal lattice, demonstrating robust edge states and topological transitions induced by helical waveguide modulation, offering a new platform for topological fractal physics.

Contribution

It presents the first realization of topological insulators in a fractal lattice with helical waveguides, showing topological edge states and robust transport in a fractal dimension.

Findings

Existence of topological edge states with real-space Chern number 1

Wavepackets propagate along edges without backscattering or bulk penetration

Robust edge transport in high-generation fractal lattices

Abstract

We present Floquet fractal topological insulators: photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides. The helical modulation induces an artificial gauge field and leads to the trivial-to-topological transition. The quasienergy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1. We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder. In a similar vein, we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation. Finally, we find topological edge-states that span the circumference of a hybrid half-fractal half-honeycomb lattice, passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering, despite the transition from two-dimensions to a fractal dimension. Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.