Trembling motion of the wave packet in armchair graphene nanoribbons (AGNRs)

Abstract

A treatment of the trembling motion or Zitterbewegung (ZB) phenomena in the armchair graphene nanoribbons (AGNRs) by using long-wave approximation is presented theoretically. We are first interested to study the time dependence of the average values for the current density in AGNR. The longitudinal and transversal components of the current density operator are derived analytically in the Heisenberg representation. The wave packet in a Gaussian distribution is considered with half-width d and a carrier wave vector in the longitudinal orientation k[Formula: see text]. The average values of the current density which represent the current induced by the motion of the electrons along the nanoribbon are calculated numerically. The interference between two energy branches, or the corresponding upper and lower energy states, leads to the trembling motion in the armchair graphene nanoribbon, and hence, our results emphasized that the phenomena of ZB has an aperiodic and nontransient oscillation in the longitudinal and transversal direction, respectively. The average values for the current density for AGNRs are calculated with extremely large value of N and compared with infinite pristine graphene.