Oscillating Guided Modes in Graphene-Based Asymmetric Waveguides

We investigate the guided modes in monolayer graphene-based waveguides with asymmetric quantum well structure induced by unequal dc voltages. The dispersion relation for the guided modes is obtained analytically, the structures of the guided modes are discussed under three distinct cases. For the cases of the classical motion and the Klein tunneling, the asymmetric structure does not influence the mode structures dramatically compared with that in the symmetric waveguide. But for the mixing case of the former two, the mode structures and the motion characteristics for the electron and the hole exhibit different behaviors at same condition. The results may be helpful for the practical application of graphene-based quantum devices.