We show analytically that the ability of Dirac materials to localize an electron in both a barrier and a well can be utilized to open a pseudo-gap in graphenes spectrum. By using narrow top-gates as guiding potentials, we demonstrate that graphene bipolar waveguides can create a non-monotonous one-dimensional dispersion along the electron waveguide, whose electrostatically controllable pseudo-band-gap is associated with strong terahertz transitions in a narrow frequency range.
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