We employ the tight-binding propagation method to study Klein tunneling andquantum interference in large graphene systems. With this efficient numericalscheme, we model the propagation of a wave packet through a potential barrierand determine the tunneling probability for different incidence angles. Weconsider both sharp and smooth potential barriers in n-p-n and n-n' junctionsand find good agreement with analytical and semiclassical predictions. When wego outside the Dirac regime, we observe that sharp n-p junctions no longer showKlein tunneling because of intervalley scattering. However, this effect can besuppressed by considering a smooth potential. Klein tunneling holds forpotentials changing on the scale much larger than the interatomic distance.When the energies of both the electrons and holes are above the Van Hovesingularity, we observe total reflection for both sharp and smooth potentialbarriers. Furthermore, we consider caustic formation by a two-dimensionalGaussian potential. For sufficiently broad potentials we find a good agreementbetween the simulated wave density and the classical electron trajectories.
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