Localized Plasmons in One Dimensional Topological Systems

One dimensional topological systems (the Schrieffer-Su-Hegger model and the generalized Aubry-André-Harper model) support strongly localized electronic states in the topologically nontrivial phases. In this work, we study plasmon modes in these systems by calculating the real space dielectric function within the random phase approximation. We observe localized plasmon modes in the electron energy loss spectra. In the topologically nontrivial sectors, these localized plasmon modes are shown to originate from the localized electronic edge states by separating the full polarization into contributions from pure bulk transitions without localized electronic states and edge-bulk transitions involving localized electronic states. We also show that the Coulomb interaction plays a role of delocalizing plasmons due to its long-range property. Therefore, the localization of plasmon modes is less strong than the localized electronic states obtained from non-interacting tight binding models.