Study of Phase Velocity and Magneto Plasmon Dispersion on the Surface of Carbon Nanotubes in Low Energy State

Abstract

Several authors have worked on theoretical and experimental plasmon excitations. The researchers have been studying the dispersion relation of magneto plasmon in the low energy state on a cylindrical surface of carbon nanotube obtained with the help of linear-angular momentum transfer. Here, we demonstrate the Dirac-like Hamiltonian equation for carbon nanotubes in the presence and absence of a parallel applied magnetic field. We assume the cylindrical carbon nanotube is infinitesimally narrow, if we reduce the bandwidth the radius of the cylindrical tube is increased in presence of a magnetic field. In this study, we find the relation between energy eigenfunction and electron wave function and discuss the properties of carbon nanotube concerning the Fermi-energy level which is induced by the applied magnetic field is obtained numerically by integrating first and second-order differential equations. We chose the Fermi energy level above the gap at E_F = 1.5 eV and below the gap at E_F = −5 eV. We see that Magneto Plasmon excitations at both levels of low and high-frequency modes. This study provides information about the electron state in carbon nanostructures and their electronic properties.