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Modes splitting in graphene-based double-barrier waveguides

The graphene-based double-barrier waveguides induced by electric field have been investigated. The guided modes can only exist in the case of Klein tunneling, and the fundamental mode is absent. The guided modes in the single-barrier waveguide split into symmetric and antisymmetric modes with different incident angles in the double-barrier waveguide. The phase difference between electron states and hole states is also discussed. The phase difference for the two splitting modes is close to each other and increases with the order of guided modes. These phenomena can be helpful for the potential applications in graphene-based optoelectronic devices.