Collective excitations in a linear periodic array of cylindrical nanotubes

A theory of collective plasma excitations in a linear periodic array of multishell nanotubes is presented. The electron system in the nanotubes is modeled by a quasifree electron gas confined to the surface of an infinitely long cylinder. The plasmon dispersion equation is derived in the random-phase approximation neglecting the electron tunneling between the individual cylindrical tubules. The dispersion equation is solved numerically for a single-wall nanotube array, and the plasmon excitation energies are obtained as a function of the wave vector in the direction of the nanotube axes and in the transverse direction. It is found that the intertube Coulomb interaction couples the modes with different angular momenta m in individual nanotubes and, in particular, lifts the $\pm m$ degeneracy of the single-nanotube modes. This effect is analyzed numerically as a function of the separation between the tubules. We show that the translational symmetry of the lattice is maintained in the plasmon spectrum, and the plasmon energies have a periodic dependence on the transverse wave vector.