Resonance Transitions in the Cylindrical Barrier as Related Carbon Nanotube States

The solution of the Schrödinger equation in a cylindrical coordinate system is considered. The carbon nanotube is modeled by a cylindrical tunnel barrier with periodic boundary conditions. An expression is obtained for the charge current depending on the radius and length of the nanotube. Shown that the current vector has a radial component that changes the sign for certain transitions with large index values. The occurrence of negative values of the current component indicates the presence of negative differential conductivity for these transitions. The appearance of additional current peaks serves as an indication of the excitation of the tunnel system by the external field. This makes it possible to further tune into resonance, which can be carried out by adjusting the “longitudinal” component of the current, depending on the length of the nanotube.