Ideal Weyl Semimetals in the Chalcopyrites ${\mathrm{CuTlSe}}_2$, ${\mathrm{AgTlTe}}_2$, ${\mathrm{AuTlTe}}_2$, and ${\mathrm{ZnPbAs}}_2$

Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites ${\mathrm{CuTlSe}}_2$, ${\mathrm{AgTlTe}}_2$, ${\mathrm{AuTlTe}}_2$, and ${\mathrm{ZnPbAs}}_2$ are ideal Weyl semimetals, having largely separated Weyl points ($\sim 0.05{\AA }^{-1}$) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-power and high-speed electronics.

Figure 1

Crystal structure and Brillouin zone (BZ). (a) The crystal structure of chalcopyrite compounds $AB{C}_2$, including ${\mathrm{CuTlSe}}_2$, ${\mathrm{CuTlTe}}_2$, ${\mathrm{AgTlTe}}_2$, ${\mathrm{AuTlTe}}_2$, ${\mathrm{ZnPbAs}}_2$, and ${\mathrm{ZnPbSb}}_2$. The deviation of $C$ atom (green) away from the center of the tetrahedron formed by $A$ and $B$ atoms is denoted by $\delta u$. (b) The top view of the chalcopyrite structure. The twofold rotation symmetries ($C_{2x}$ and $C_{2y}$) and the two mirror symmetries ($M_{xy}$ and $M_{-xy}$) are marked. (c) The BZ of chalcopyrite compounds.

Figure 2

Band structure and Weyl points. (a) The bands of ${\mathrm{CuTlTe}}_2$ without turning on the spin-orbit coupling (SOC) effect. The $p_z$ bands are below $p_{x,y}$ bands at the $\mathrm{\Gamma }$ point. (b) The bands of ${\mathrm{CuTlTe}}_2$ with turning on the SOC effect. An energy gap opens along the line of $\mathrm{\Gamma }\text{−}Z$, and one Weyl point is seen between $\mathrm{\Gamma }$ and $Z^{\prime }$. $E_{\text{Weyl}}$ denotes the energy level of Weyl points. (c) The bands of ${\mathrm{Hg}}_2{\mathrm{Te}}_2$ without turning on the SOC effect at the $\mathrm{\Gamma }$ point are threefold degenerate protected by the cubic symmetry. (d) The schematic eight symmetry-related Weyl points in the BZ. (e) Berry curvature in a $k_z$ plane including four Weyl points. The Weyl points at $(\pm k_x^{*},0,\pm k_z^{*})$ have the $-1$ chirality and at $(0,\pm k_y^{*},\pm k_z^{*})$ have $+1$ chirality.

Figure 3

Surface states and Fermi arcs. (a) The LDOS for ${\mathrm{CuTlTe}}_2$ projected onto the (001) surface. The warmer colors represent a higher LDOS. The red (blue) regions indicate bulk bands (energy gaps), and the single red lines indicate the surface states. The bulk band crossing ($\overline{k_x^{*}}$, 0), projected from the two Weyl points ($k_x^{*}$, 0, $\pm k_z^{*}$), can be seen in the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ line. The velocities of surface states along $\overline{\mathrm{\Gamma }}\text{−}{\overline{M}}_1$ and $\overline{\mathrm{\Gamma }}\text{−}{\overline{M}}_2$ have opposite sign. (b) A closed Fermi surface consists of four Fermi arcs in the (001) surface. The high-symmetry lines in (a) are marked. (c) The open Fermi arcs on the (010) surface. (d) The enlarged Fermi arcs of (c).

Figure 4

Band structures of Weyl semimetal candidates. (a–f) The band structures with turning on the SOC effect by the MBJ calculations for ${\mathrm{CuTlSe}}_2$ (a), ${\mathrm{CuTlTe}}_2$ (b), ${\mathrm{AgTlTe}}_2$ (c), ${\mathrm{AuTlTe}}_2$ (d), ${\mathrm{ZnPbAs}}_2$ (e) and ${\mathrm{ZnPbSb}}_2$ (f).