The effect of a velocity barrier on the ballistic transport of Dirac fermions

We propose a novel way to manipulate the transport properties of massless Dirac fermions by using velocity barriers, defining the region in which the Fermi velocity, $v_{F}$, has a value that differs from the one in the surrounding background. The idea is based on the fact that when waves travel accross different media, there are boundary conditions that must be satisfied, giving rise to Snell's-like laws. We find that the transmission through a velocity barrier is highly anisotropic, and that perfect transmission always occurs at normal incidence. When $v_{F}$ in the barrier is larger that the velocity outside the barrier, we find that a critical transmission angle exists, a Brewster-like angle for massless Dirac electrons.