Theoretical Treatment of the Zitterbewegung phenomena in the multilayer armchair graphene nanoribbons (MLAGNRs)

Abstract A treatment of Zitterbewegung (ZBW) phenomena in the multilayers armchair graphene nanoribbons (MLAGNRs) is presented theoretically by using long-wave approximation. Firstly, the time dependence of the average values of the position operators in the both longitudinal and transversal orientations are evaluated in MLAGNRs. The longitudinal and transversal components of the position operators derived analytically by using the Heisenberg representation. The Gaussian distribution of the wave packet is considered with the longitudinal carrier wave number kxo. The interference between the valence and the conduction energy bands, leads to the emergence the Zitterbewegung phenomena in the MLAGNRs, however, the presentes results emphasized that this phenomena has a transient, aperiodic and irregular oscillation in the longitudinal and transversal orientations. The average values of the position operators for MLAGNRs is calculated for three values of N (N = 5, 10 and 15).