The influence of external transverse magnetic field in propagation of electrostatic oscillations in single-walled carbon nanotubes

Propagation of an electrostatic oscillation by using the linearized quantum hydrodynamic model in conjunction with Maxwell's equations was studied. The dispersion relation of a system of electron plasma in single-walled carbon nanotubes in the presence of an external magnetic field B-0 by considering the exchange-correlation effects in 2D cylindrical geometry is derived here. The uniform static magnetic field is assumed to be normal to the cylindrical surface (Voigt configuration). Distribution of the electrons and ions are considered uniformly over the cylindrical surface of a nanotube. It is found that the external magnetic field has significant impact on the wave in the longer wavelength. The influence of variation in azimuthal index and radius of the nanotube on dispersion relation is also discussed. It is tried to plot some schemes and analyze numerically in different limits of cylindrical and planar geometries. The results can be important in the study of collective phenomena in nanostructures.