Electronic collective excitations in thin toroids

The elementary excitations of electron gases confined to a toroid system are studied within the random-phase approximation. They strongly depend on the angular momentum (L), the toroid geometry (radius and height), and the intertoroid coupling. The angular momentum is conserved in the electron-electron interactions, owing to the cylindrical symmetry. The electronic collective excitations (plasmons) of different L's are thus mutally decoupled. The plasma oscillation for a giving L behaves as a standing wave on a toroid of radius R, which occurs at the discrete wavelength 2π R/L. Intertoroid interaction for two parallel toroids has been included. It causes two plasmon branches for each L. The plasmon with the higher frequency will exhibit the relatively pronounced excitation spectrum.