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Motivated by the realization of the Dirac point with tunable Fermi velocity in low-dimensional systems, we investigate the guided modes in graphene waveguides corresponding to the electron motion (or the hole motion) in a symmetric velocity barrier. We find that the fundamental mode always exists, but the higher-order mode may disappear. These discrete guided modes imply that there is a lowest cutoff frequency for an incident electron and that the incident electrons with different angles may have different minimum cutoff frequencies. These interesting features will be helpful for the investigation on an electronic fiber.

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