Topological states in disordered arrays of dielectric nanoparticles

TL;DR

This paper investigates how disorder affects topological edge states in zigzag arrays of dielectric nanoparticles, revealing new phase transitions and robustness of spectral gaps in staggered-spacing configurations.

Contribution

It introduces a detailed analysis of topological phases in disordered nanoparticle arrays, highlighting the effects of spacing patterns and disorder on edge states and phase transitions.

Findings

Equal-spacing arrays show edge localization with disorder, consistent with experiments.

Staggered-spacing arrays exhibit richer topological phases with multiple winding numbers.

Disorder induces phase transitions and can preserve spectral gaps in staggered arrays.

Abstract

We study the interplay between disorder and topology for the localized edge states of light in topological zigzag arrays of resonant dielectric nanoparticles. We characterize topological properties by the winding number that depends on both zigzag angle and spacing between nanoparticles in the array. For equal-spacing arrays, the system may have two values of the winding number $\nu=0$ or $1$, and it demonstrates localization at the edges even in the presence of disorder, being consistent with experimental observations for finite-length nanodisk structures. For staggered-spacing arrays, the system possesses richer topological phases characterized by the winding numbers $\nu=0$, $1$ or $2$, which depend on the averaged zigzag angle and disorder strength. In a sharp contrast to the equal-spacing zigzag arrays, staggered-spacing arrays reveal two types of topological phase transitions induced by the angle disorder, (i) $\nu = 0 \leftrightarrow \nu = 1$ and (ii) $\nu = 1 \leftrightarrow \nu = 2$. More importantly, the spectrum of staggered-spacing arrays may remain gapped even in the case of a strong disorder.