Dirac semimetals $A_3\text{Bi}$ $\left(A=\text{Na},\text{K},\text{Rb}\right)$ as ${\mathbb{Z}}_2$ Weyl semimetals

We demonstrate that the physical reason for the nontrivial topological properties of Dirac semimetals $A_3\mathrm{Bi}$ $\left(A=\mathrm{Na},\mathrm{K},\mathrm{Rb}\right)$ is connected with a discrete symmetry of the low-energy effective Hamiltonian. By making use of this discrete symmetry, we argue that all electron states can be split into two separate sectors of the theory. Each sector describes a Weyl semimetal with a pair of Weyl nodes and broken time-reversal symmetry. The latter symmetry is not broken in the complete theory because the time-reversal transformation interchanges states from different sectors. Our findings are supported by explicit calculations of the Berry curvature. In each sector, the field lines of the curvature reveal a pair of monopoles of the Berry flux at the positions of Weyl nodes. The ${\mathbb{Z}}_2$ Weyl semimetal nature is also confirmed by the existence of pairs of surface Fermi arcs, which originate from different sectors of the theory.

Figure 1

The projection of the Berry curvature ${\mathbf{F}}_{++}\left(\mathbf{k}\right)$ (left panel) and ${\mathbf{F}}_{--}\left(\mathbf{k}\right)$ (right panel) on the $k_y=0$ plane.

Figure 2

The surface Fermi arcs for $\alpha =1\text{eV}{\text{Å}}^3$ and energy $E=0,\pm 50,\pm 100$ meV.