Exact long-wavelength plasmon dispersion on a ring with soft Coulomb interactions

We obtain the analytical dispersion of 1D plasmonic modes on a ring from the exact solution of the hydrodynamical model with soft Coulomb potential. We compare our results with the exact plasmon dispersion in straight 1D systems and find a set of formal correspondences between the two. In light of our results, we discuss recent experiments (Schmidt et al 2014 Nat. Commun. 5 3604) where ring-confined modes in nanodiscs are found to almost coincide with plasmonic excitations in 1D metallic nanostructures. We trace the similarity to the scaling properties of the plasmonic dispersion.