Theoretical Examination of the Trembling Motion of Dirac Electrons on the Surfaces of Single and Multilayer Armchair Graphene Nanoribbons

The phenomenon of trembling motion, known as Zitterbewegung (ZBW) in German, has intrigued scientists for many years. This research report offers a theoretical analysis of this occurrence in armchair-type graphene strips using the long-wave model, determining the position operator for the ࢞ෝ and ࢟ෝ directions according to the Heisenberg representation. The Gaussian distribution function was used as a representation of the pseudo-spin wave function. The influence of the graphene nanoribbon's width and the wave vector kx on the oscillation values of this phenomena, together with the multiplicity of graphene layers, was examined. This particular graphene nanoribbon was selected because to its minimal edge effects, allowing it to function as a semiconductor material with a controllable energy gap. Consequently, this phenomenon may be realised via the interference between the conduction and valence energy bands. A series of analytical and numerical mathematical computations were performed, resulting in the following findings: This phenomenon was first seen in this sort of graphene nanoribbons, occurring within around 30 femtoseconds for both orientations and varying values of ࢻ and ࢼ. The hexagonal graphene lattice has a likelihood of harbouring electrons. Secondly, the findings indicated that the oscillation of the electron wave packet is transitory and bidirectional, exhibiting semi-regular periodicity for widths of ࡹ ૞ = and ࡹ ૙૚ = across all layers. The oscillation value rises as the breadth of the wave packet diminishes. Thirdly, when the number of graphene layers rises, an area referred known as the Astrach region emerges owing to electron transport between the layers. The influence of the hopping energy parameter is evident here. This study work offers theoretical insights into the Zitterbewegung phenomena in graphene strips, representing a modest addition to the field.