Monopole mining method for high-throughput screening for Weyl semimetals

Although topological invariants have been introduced to classify the appearance of protected electronic states at surfaces of insulators, there are no corresponding indices for Weyl semimetals whose nodal points may appear randomly in the bulk Brillouin zone (BZ). Here we use a well-known result that every Weyl point acts as a Dirac monopole and generates integer Berry flux to search for the monopoles on rectangular BZ grids that are commonly employed in self-consistent electronic structure calculations. The method resembles data mining technology of computer science and was demonstrated on locating the Weyl points in known Weyl semimetals. It was subsequently used in high-throughput screening of several hundreds of compounds and predicting a dozen materials hosting nodal Weyl points and/or lines.

Figure 1

(a) A typical cone dispersion relationship $E\left(\mathbf{k}\right)=\pm v|\mathbf{k}-{\mathbf{k}}_{WP}|$ for the Weyl point plotted within a rectangular area in $k$ space set by divisions of reciprocal lattice translations ${\mathbf{G}}_1$ and ${\mathbf{G}}_2$ for a fixed value along the third translation ${\mathbf{G}}_3$. (b) The Weyl point located within a microcell set by the grid vectors ${\mathbf{q}}_1,{\mathbf{q}}_2,{\mathbf{q}}_3$ generates a Berry flux through each plaquette as given by the (right handed) circulation of the Berry connection with sign convention defined in text.

Figure 2

ZrNiAl-type crystal structure (no. 189 space group $p\overline{6}2m$) of noncentrosymmetric hexagonal compounds studied in this work.

Figure 3

(a) Positions of 6 pairs (cyan for chiral positive and magenta for chiral negative) of low-energy Weyl points seen along the $\mathrm{\Gamma }M$ direction in the BZ for LaInMg and referenced in Table 2 as sort A; (b) Positions of 12 pairs of Weyl points that are shifted symmetrically away from the $\mathrm{\Gamma }K$ line for HfPRu and referenced in Table 2 as sort B; (c) A set of nodal lines for TiGePd that is recovered by the monopole mining method presented in this work. The color (cyan and magenta) distinguishes chiral positive and negative lines, respectively. The zoomed area of the BZ is bounded by $0.15\le 2\pi k_z/c\le 0.22$ and $-0.03\le 2\pi k_{x,y}/a\le +0.03.$ Also shown in yellow are the triple degenerate topological points [41].