Zak phase and zero extinction of topologically protected edge states in PT-symmetric plasmonic chains

By considering parity-time (PT) symmetric plasmonic chains, an array of plasmonic nanoparticles coated alternatively by gain-loss balanced dielectrics, we demonstrate that it supports topological edge states with quantized Zak phase when there is no exceptional point in the entire Brillouin zone (BZ). We show that the coupled dipole equation of the system can be reduced to a 2 by 2 Eigenvalue problem, with next nearest neighbor approximation and neglecting radiation loss. Due to the PT symmetry, the two edge states' plasmon resonant frequencies are complex conjugates of each other, and they give zero optical extinction when they are simultaneously excited by plane waves polarized along the chain axis. Results are numerically confirmed by multipole scattering theory.