Low-energy magnetoplasmon excitations in semimetallic carbon nanotubes

The low-energy electron spectrum of semimetallic carbon nanotubes consists of two pairs of electron and hole subbands with linear dispersion intersecting at the Fermi level. An external perturbation such as a magnetic or electric field lifts the degeneracy of the subbands and opens a minigap at the band crossing. A quasi-one-dimensional massless Dirac-like Hamiltonian has been used to model the low-energy electron spectrum of this system as a function of the wave vector along the nanotube axis. Within this model, the plasmon dispersion formula is obtained for the arbitrary allowed angular- and linear-momentum transfer. The plasmon energies are calculated as a function of the transferred momentum and the nanotube radius when there is no transferred angular momentum. We show that both the low-frequency (quasiacoustic) and the high-frequency (optical) plasmon excitations are obtained in this system, depending on the position of the Fermi level with respect to the energy gap induced by the external perturbation. We calculate the phase velocity C_p as a function of the Fermi level. Our results show that C_p has kinks that are due to an increased density of states within the band. There is a discontinuity in the curve near which the minigap opens up.