Ishaya Iliyasu
The collective oscillation of electrons in a nanotube was investigated theoretically. Kubo formula was analytically derived for electron gas conductivity tensor on the surface of a nanotube in a magnetic field. The plasma wave spectrum of an electron gas on a cylindrical surface with longitudinal superlattice was determined using the hydrodynamic approximation methods, considering time and spatial dispersion. Within the framework of this approach Poisson equation, continuity equation and constitutive equations were considered and the dispersion equation was obtained for the spectrum of plasma waves on the surface of a nanotube. The plasma waves, interband current and the spectra of waves on a semiconductor nanotube surface were considered. Because of the dispersion equation parameter in the spectrum of Plasma there exists, either one branch of the spectrum or two branches. The first branch describes optical Plasmon due to anti-phase oscillations of the electron density in the mini-bands involved in the transitions. The second branch of the acoustic is due to in phase oscillations of the electrons in the mini-bands. The study showed that the Plasma waves experiences Landau damping.
