Effect of the Width of The Single-Layer Graphene Nanoribbon on the Trembling Motion of Dirac Electrons

This work presents a theoretical investigation of the Zitterbewegung (ZBW) phenomenon- an intrinsic trembling motion of Dirac electrons- in armchair-type multilayer graphene nanoribbons (AGNRs). Utilizing the long-wavelength approximation and the Heisenberg representation, the study explores the time evolution of the position operator for electrons described by Gaussian wave packets. Key physical parameters, including ribbon width, initial wave vector, and pseudo-spin polarization, are systematically varied to analyze their impact on the characteristics of ZBW oscillations. The results reveal that ZBW is highly sensitive to these factors, with oscillations occurring within ultrashort timescales (~30 femtoseconds). Notably, wider ribbons and broader wave packets lead to reduced oscillation amplitudes. The role of pseudo-spin configuration is found to be crucial in enabling or suppressing the oscillatory behavior. These findings offer deeper insight into the relativistic-like quantum dynamics of electrons in graphene nanostructures and suggest potential implications for future applications in ultrafast nanoelectronics and quantum devices.