Electronic states in heterostructures with piece-wise uniform Dirac cones

Abstract

We discuss graphene physics that are associated with Fermi velocity rather than bandgap or external potential. Such physics are illustrated with a simple junction that is comprised of two uniform electrodes bridged by a central uniform channel. The main difference between these components is supposed to come at their Fermi velocities (Dirac cone slopes), which take different values: ν0 in the electrodes and v in the channel. This junction can be fabricated, for example, by depositing a single-layer graphene on prepatterned substrate. Both scattering states and localized states have been explored. Making full analog with optics, the discussions have been focused on these aspects: refraction, total internal reflection (TIR), and transmission. Regarding them, Snell’s law and the TIR critical angle have been derived and the TIR impacts on transmission have been calculated. Potential applications of this junction have been discussed. In particular, we found that, an electrical switch and an electron box can be made of it.