Klein tunneling and electron optics in Dirac-Weyl fermion systems with tilted energy dispersion

The transport properties of relativisticlike fermions have been extensively studied in solid-state systems with isotropic energy dispersions. Recently, several two-dimensional and three-dimensional Dirac-Weyl (DW) materials exhibiting tilted energy dispersions around their DW cones have been explored. Here, we demonstrate that such a tilt character could induce drastically different transport phenomena, compared to the isotropic-dispersion cases. Indeed, the Klein tunneling of DW fermions of opposite chiralities is predicted to appear along two separated oblique directions. In addition, valley filtering and beam splitting effects are easily tailored by dopant engineering techniques whereas the refraction of electron waves at a (p-n)-doped interface is dramatically modified by the tilt, thus paving the way for emerging applications in electron optics and valleytronics.