Ballistic transport through graphene nanostructures of velocity and potential barriers

We investigate the electronic properties of graphene nanostructures when the Fermi velocity and the electrostatic potential vary in space. First, we consider the transmission T and conductance G through single and double barriers. We show that G for velocity barriers differs markedly from that for potential barriers for energies below the height of the latter and it exhibits periodic oscillations as a function of the energy for strong velocity modulation. Special attention is given to superlattices (SLs). It is shown that an applied bias can efficiently widen or shrink the allowed minibands of velocity-modulated SLs. The spectrum in the Kronig-Penney limit is periodic in the strength of the barriers. Collimation of an electron beam incident on an SL with velocity and potential barriers is present but it disappears when the potential barriers are absent. The number of additional Dirac points may change considerably if barriers and wells have sufficiently different Fermi velocities.