Guided modes in graphene waveguides

By analogy of optical waveguides, we investigate the guided modes in graphene waveguides, which is made of symmetric quantum well. The unique properties of the graphene waveguide are discussed based on the two different dispersion relations, which correspond to classical motion and Klein tunneling, respectively. It is shown that the third-order mode is absent in the classical motion, while the fundamental mode is absent in the Klein tunneling case. We hope these phenomena can lead to the potential applications in graphene-based quantum devices.