Topological states in disordered arrays of dielectric nanoparticles

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, ν=0 or ν=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 ν=0, ν=1, or ν=2, which depend on the averaged zigzag angle and the strength of disorder. In a sharp contrast to the equal-spacing zigzag arrays, the staggered-spacing nanoparticle arrays support two types of topological phase transitions induced by the angle disorder, (i) ν=0↔ν=1 and (ii) ν=1↔ν=2. More importantly, the spectrum of the staggered-spacing nanoparticle arrays may remain gapped even in the case of a strong disorder.