Influence of Fermi arc states and double Weyl node on tunneling in a Dirac semimetal

Most theoretical studies of tunneling in Dirac and the closely related Weyl semimetals have modeled these materials as single Weyl nodes described by the three-dimensional Dirac equation $H = v_f \vec{p}\cdot\vec{\sigma}$. The influence of scattering between the different valleys centered around different Weyl nodes, and the Fermi arc states which connect these nodes are hence not evident from these studies. In this work we study the tunneling in a thin film system of the Dirac semimetal $\text{Na}_3\text{Bi}$ consisting of a central segment with a gate potential, sandwiched between identical semi-infinite source and drain segments. The model Hamiltonian we use for $\text{Na}_3\text{Bi}$ gives, for each spin, two Weyl nodes separated in $k$-space symmetrically about $k_z=0$. The presence of a top and bottom surface in the thin film geometry results in the appearance of Fermi arc states and energy subbands. We show that (for each spin) the presence of two Weyl nodes and the Fermi arc states result in enhanced transmission oscillations, and finite transmission even when the energy falls within the \textit{bulk} band gap in the central segment respectively. These features are not evident in single Weyl node models.