“…Our results provide insightful information about the underlying properties of the EPs in flatband systems. In future works, it will be also interesting to investigate a wide range of phenomena such as the topological transitions and nonlinear optical processes associate with the higher-order EPs [57][58][59][60]. Here, we will provide an analytical study into the eigenvalue evolutions of the PT -symmetric photonic structure in the vicinity of the EP3.…”