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

Abstract

The outstanding electronic properties of relativistic-like fermions have been extensively studied in solid state systems with isotropic linear dispersions such as graphene. Here, we show that 2D and 3D Dirac-Weyl (DW) materials exhibiting tilted energy dispersions could induce drastically different transport phenomena, compared to the non-tilted case. 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 while the refraction of electron waves is dramatically modified by the tilt, thus paving the way for emerging applications in electron optics and valleytronics.