Synthetic Weyl points in plasmonic chain with simultaneous inversion and reflection symmetry breaking

Photonic nanoparticle arrays present a unique platform for exploring optical topological phenomena. In this study, we incorporate the concept of synthetic dimensions into the plasmonic system, which allows us to investigate Weyl physics within a chain of metallic nanoparticles. By introducing two extra periodic positional parameters into the chain, we construct a synthetic three-dimensional space that gives rise to synthetic Weyl points (WPs). Our findings reveal that the chain maintains topologically protected edge modes even when the inversion symmetry of the chain is broken. The topological properties of these edge modes are intrinsically linked to the WPs within the synthetic three-dimensional space. However, degenerate edge modes emerge exclusively in chains possessing inversion symmetry. Furthermore, we uncover the bulk-edge correspondence in the chains, yielding a deeper understanding of the topological nature of edge modes in systems without symmetry. Our research not only clarifies the topological origin of a class of edge states within asymmetric nanoparticle chains but also provides perspectives for realizing higher-dimensional topological effects in nanoparticle arrays.