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 id
ea is based on the fact that when waves travel accross different media, there are boundary conditions that must be satisfied, giving rise to Snells-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.
By analyzing the strength of a photon-fermion coupling using basic scattering processes we calculate the effect of a velocity anisotropy on the critical number of fermions at which mass is dynamically generated in planar QED. This gives a quantitativ
e criterion which can be used to locate a quantum critical point at which fermions are gapped and confined out of the physical spectrum in a phase diagram of various condensed matter systems. We also discuss the mechanism of relativity restoration within the symmetric, quantum-critical phase of the theory.
