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Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tight-binding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schrodinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.

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