Topological states in disordered arrays of dielectric nanoparticles

Abstract

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