waveguides based on graphene. We find the spectra of the two-dimensional (2D) Dirac-like
Hamiltonian with a quasi-mass parameter β, which is incorporated into the Hamiltonian in an
ad hoc manner. Such a term can represent phenomenologically the spin–orbit interaction
strength in the graphene sample. We found strongly coupled modes as the wavevector ky
increased. We show that different choices for the parameter β in both waveguides induce …