Surface Fermi arcs in ${\mathbb{Z}}_2$ Weyl semimetals $A_3\mathrm{Bi}$ ($A=\mathrm{Na}$, K, Rb)

The surface Fermi arc states in ${\mathbb{Z}}_2$ Weyl semimetals $A_3\mathrm{Bi} (A=\mathrm{Na},\mathrm{K},\mathrm{Rb})$ are studied by employing a continuum low-energy effective model. It is shown that the surface Fermi arc states can be classified with respect to the ud-parity symmetry. Because of the symmetry, the arcs come in mirror symmetric pairs. The effects of symmetry breaking terms on the structure of the Fermi arcs are also studied. Among other results, we find at least two qualitatively different types of the surface Fermi arcs. The arcs of the first type link disconnected sheets of the bulk Fermi surface, while arcs of the second type link different points of the same bulk Fermi surface sheet.

Figure 1

The bottom surface Fermi arcs for several different values of the Fermi energy in a simplified two-component model, described by Hamiltonian (16) with $C_2=M_2=0$. The analytical form of the arcs is given in Eq. (21).

Figure 2

The bottom surface Fermi arcs (25) for several values of the Fermi energy in a two-component model, described by Hamiltonian (16) with $C_2\ne 0$ and $M_2\ne 0$.

Figure 3

The Fermi arcs solutions in the plane of transverse momenta for $\alpha =1\text{eV}{\text{Å}}^3$ (left) and $\alpha =50\text{eV}{\text{Å}}^3$ (right).

Figure 4

The Fermi arcs solutions (thick black lines) in the model with the symmetry breaking parameters $m_1$ and ${\tilde{\mu }}_1$ at $E=0$. The shaded regions represent the projections of the bulk Fermi surfaces onto the $k_x{k}_z$ plane. The values of $m_1$ and ${\tilde{\mu }}_1$ are given in units of ${\text{Å}}^{-2}$ and $\text{eV}$, respectively.