Fig. 2: Nodal line semimetal and Weyl semimetal phases for different vector chirality (κ = ‘ ± 1’) states.

a, b Band structures calculated with spin-orbit coupling for a particular κ = + 1 and − 1 magnetic states, respectively. The k-path segments are shown in Fig. 1b. c, d 3D band structures for κ = + 1 and − 1, respectively calculated within kz = 0 plane. The red line drawn along the band crossings defines the nodal-ring state whose projection on a constant energy plane is an ellipse.