Photonic Floquet topological insulators in a fractal lattice

Zhaoju Yang,Yaakov Lumer,Mordechai Segev,Eran Lustig

doi:10.1038/s41377-020-00354-z

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 a trivial-to-topological phase transition. The quasi-energy 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.

Highlights

Topological insulators are a new phase of matter characterized by an insulating bulk and perfectly conductive edges[1,2]
Photonics has become the cutting-edge platform for exploring all kinds of topological phases ranging from the quantum spin Hall effect[12], Floquet topological insulators[13], topological crystalline insulator[16], and valley Hall effect[17,18]; all the way to topological systems that lack periodicity, such as topological quasicrystals[19] and even topological Anderson insulators, in which the topology is induced by disorder[20]
We focus on fractal lattices of generations G(4) and G(5), and we conjecture that the conclusions we draw from this study hold for the Sierpinski gasket (SG) lattice in any generation

Summary

Introduction

Topological insulators are a new phase of matter characterized by an insulating bulk and perfectly conductive edges[1,2]. Floquet spectrum and show the existence of topological edge states corresponding to real-space Chern number 124,25, which can be controlled by periodic driving.

Results

Conclusion