COLLECTIVE EXCITATIONS IN METALLIC GRAPHENE TUBULES

The collective modes of coaxial-graphene-tubule systems are calculated using both classical and quantum-mechanical approaches. While the der ived results are valid for any number of coaxial tubules, the numerica l results for the dispersion relations of the plasmons are presented f or a system consisting of four graphene tubules for various values of the azimuthal quantum number m. The lowest modes (m=0) are found to be quasiacoustic, like the one-dimensional plasmons, whereas the higher modes are of optical nature. For each m, the number of observable mode s is equal to the number of tubules having a metallic character. The e ffect of the intertubule interactions is a broadening of the frequency range of the m modes. This broadening remains important so long as th e plasmon momentum is significantly smaller than the Fermi momentum.