Electric and magnetic waveguides in graphene: quantum and classical

Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. We have assumed the displacement symmetry of the system along the y-direction, whose associated constant is k. We have also examined other symmetries relevant to each type of waveguide, magnetic or electric. Waveguides with square profile have been worked out in detail to show up explicitly some of the most interesting features. For example, the classical region of confined motion of the electric case, for a fixed intensity, is bounded between k and -k, while in the magnetic case that region is symmetric in the energy and presents a gap (-k, k). Besides, in the quantum systems we have shown that there are edge states in the magnetic systems but they are missing in electric waveguides. We have also analysed scattering states and resonances which match with bound states for both waveguides. The classical scattering properties are also quite different in both types of waveguides. While the electric system has essentially one type of refraction of the incident electron, the magnetic system is much richer due to the Lorentz force.