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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 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.
Quantum coherent transport of Dirac fermions in a mesoscopic nanowire of the 3D topological insulator Bi2Se3 is studied in the weak-disorder limit. At very low temperatures, many harmonics are evidenced in the Fourier transform of Aharonov-Bohm oscil
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the surface stat
Far infrared magneto-transmission spectroscopy has been used to probe relativistic fermions in highly oriented pyrolytic and natural graphite. Nearly identical transmission spectra of those two materials are obtained, giving the signature of Dirac fe
Ballistic electrons in solids can have mean free paths far larger than the smallest features patterned by lithography. This has allowed development and study of solid-state electron-optical devices such as beam splitters and quantum point contacts, w
We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives unde