Abstract
We investigate the dynamics of a charged particle moving in a graphene layer and in atwo-dimensional electron gas, where it obeys the Dirac and the Schrödinger equations,respectively. The charge carriers are described as Gaussian wavepackets. The dynamics ofthe wavepackets is studied numerically by solving both quantum-mechanical andrelativistic equations of motion. The scattering of such wavepackets by step-like magneticand potential barriers is analysed for different values of wavepacket energy and width. Wefind: (1) that the average position of the wavepacket does not coincide with the classicaltrajectory, and (2) that, for slanted incidence, the path of the centre of mass of thewavepacket does not have to penetrate the barrier during the scattering process.Trembling motion of the charged particle in graphene is observed in the absence of anexternal magnetic field and can be enhanced by a substrate-induced mass term.
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