Time evolution of current density in conducting single-walled carbon nanotubes

In the present work, we study the trembling motion known as Zitterbewegung in a conducting single-walled carbon nanotube by using the long-wave approximation. The Heisenberg representation is used to derive an analytical expression for the current density operator along the axial and spiral direction, which describes the current induced by the motion of the electronic wave packet in the carbon nanotubes. We have considered a number of parameters to describe the Gaussian wave packet, such as: the values of the initial pseudo-spin polarization, the initial carrier wave vector and the width of the localized packet along the axial and spiral coordinates. As a result, we show that the oscillation in current density can be controlled not only by the initial parameters of the wave packet, but mainly by choosing the up and low components of the localized quantum state. The analysis of the interference between the conduction and valence bands of quantum states is emphasized as the possibility of the emergence of the transient or aperiodic temporal oscillations in the average value for the current density in the conducting single-walled carbon nanotubes.