Fig. 4. All the patterns of locations of gap-closing points after parametric closing of the gap.

(A) A line node for a nodal-line semimetal. Although the figure shows the case with a single line node, the number of line nodes can be 1, 2, 3, 4, or 6. (B to P) All the patterns of Weyl nodes after parametric gap closing at k₀. Yellow and green spheres denote monopoles and antimonopoles in k space, and they are both Weyl nodes. Solid lines denote high-symmetry directions. In (G) to (O) and (Q), the z axis, taken to be perpendicular to the plane, is parallel to a high-symmetry axis. q ≡ k − k₀ is the momentum measured from k₀. In (I), (L), (M), and (N), all the Weyl nodes are coplanar with k₀, whereas in (G), (H), (J), (K), (O), and (Q), the Weyl nodes are mutually displaced along the z direction.