Theory of plasmons in carbon nanotube bundles

Abstract

We develop a suitable theoretical framework for studying plasmons in nanotube bundles. In the plane perpendicular to the tubes, the nanotubes form a two-dimensional lattice. We use a simple model of free electron gas confined to arrays of cylindrical surfaces, however the theoretical framework can also be applied to more sophisticated models for carbon nanotubes. Both intrasubband (classical) and intersubband (quantum) plasmons in such nanotube bundle systems are studied. Analytical solutions have been obtained for the case where only one subband is occupied, while numerical solutions have been obtained for the case of many occupied subbands. Intertube Coulomb coupling is found to play an intricate role, as it can both harden and soften plasmon modes in the same nanotube bundle. Intertube Coulomb coupling is also responsible for sizable plasmon dispersions in the transverse plane. All plasmons are found to be undamped by the corresponding single particle type electron-hole pair excitations. The classical plasmon exhibits three-dimensional character in the long wavelength limit, and one-dimensional character in the short wavelength limit. For quantum plasmons, the plasmon energy can be significantly larger than the corresponding single particle excitation energy between subbands. This feature is similar to quantum plasmons in semiconductor quantum wire systems.