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 film 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 $\lambda \ne 1$ leads to a breaking of rotational invariance. Furthermore, we observed that for different values of incident angle $\theta$ and anisotropy parameter $\lambda$ 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 $\lambda$. Last, we studied the case of a barrier that was placed in the linearly dispersive direction and found Klein tunneling $T-1\propto {\theta }^6+\mathcal{O}\left({\theta }^8\right)$ that is enhanced when compared to the Klein tunneling in linear Dirac semi-metals or graphene where $T-1\propto {\theta }^2+\mathcal{O}\left({\theta }^4\right)$.

受最近对真实材料 Tl(TeMo) 中各向异性立方狄拉克半金属的第一性原理预测的启发${}_3$，我们研究电子在此类系统中穿过势垒的行为。为了清楚地研究不同贡献对哈密顿量的影响，我们在各种限制下研究模型。首先，在非常薄的薄膜材料的限制中，线性色散$z$-方向在零动量处冻结，并且在 $X$——$是$平面是旋转对称的。在这个极限中，我们发现克莱因隧穿让人想起在单层石墨烯和线性色散狄拉克半金属中观察到的情况。其次，材料厚度的增加导致非零动量特征值的可能性${克}_z$它作为哈密顿量的有效质量项。我们发现这些会导致克莱因隧道效应的抑制。三、包含一个各向异性参数$\lambda \ne 1$导致旋转不变性的破坏。此外，我们观察到对于不同的入射角值$\theta$ 和各向异性参数 $\lambda$哈密​​顿量支持传播到无穷远的不同数量的模式。我们以类似于远距离探测器相图的图表形式显示这种效果。第四，我们考虑各向异性和非零的共存${克}_z$ 但没有发现非零动量之间相互作用所独有的任何影响 ${克}_z$ 和各向异性参数 $\lambda$. 最后，我们研究了放置在线性色散方向的势垒的情况，并发现了克莱因隧道$吨-1\propto {\theta }^6+\mathcal{哦}\left({\theta }^8\right)$ 与线性狄拉克半金属或石墨烯中的克莱因隧道相比得到增强，其中 $吨-1\propto {\theta }^2+\mathcal{哦}\left({\theta }^4\right)$.