Tunneling in an anisotropic cubic Dirac semi-metal

Ahmed Bouhlal; Ahmed Jellal; Hocine Bahlouli; Michael Vogl

doi:10.1016/j.aop.2021.168563

paper

Tunneling in an anisotropic cubic Dirac semi-metal

arXiv:2103.01807 · doi:10.1016/j.aop.2021.168563

Abstract

Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo) $_{3}$ , we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate effects from different contributions to the Hamiltonian we study the model in various limits. First, in the limit of a very thin material where the linearly dispersive $z$ -direction is frozen out at zero momentum and the dispersion in the $x$ - $y$ plane is rotationally symmetric. In this limit we find a Klein tunneling reminiscent of what is observed in single layer graphene and linearly dispersive Dirac semi-metals. Second, an increase in thickness of the material leads to the possibility of a non-zero momentum eigenvalue $k_{z}$ that acts as an effective mass term in the Hamiltonian. We find that these lead to a suppression of Klein tunneling. Third, the inclusion of an anisotropy parameter $λ \neq = 1$ leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle $θ$ and anisotropy parameter $λ$ the Hamiltonian supports different numbers of modes propagating to infinity. We display this effect in form of a diagram that is similar to a phase diagram of a distant detector. Fourth, we consider coexistence of both anisotropy and non-zero $k_{z}$ but do not find any effect that is unique to the interplay between non-zero momentum $k_{z}$ and anisotropy parameter $λ$ . Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling $T - 1 \propto θ^{6} + O (θ^{8})$ that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where $T - 1 \propto θ^{2} + O (θ^{4})$ .

References in corpus (129)

Cited by in corpus (1)

Tunneling phase diagrams in anisotropic Multi-Weyl semimetals