Polar interface phonons in ionic toroidal systems

We use the dielectric continuum model to obtain the polar (Fuchs–Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.