Figure 3. The topological nodal-lines in Co₂TiX in the absence spin-orbit coupling.

(a) The nodal-lines in k_x-k_y-k_z space formed by the band crossings within the majority band structure. (b) The band structure in E-k_x-k_y space containing the nodal-line on the k_z = 0 plane. On k_z = 0 plane, the bulk valence and conduction bands dip into with each other and form a energy-dependent nodal-line (the red line). (c) The energy dispersions along k_x (left panel), k_y (middle panel), and k_z (left panel) directions away from the crossing point surrounded by the black circle in panel (a). (d) Band crossings on the k_z = 0 plane. The red lines show the nodal line formed by the same (majority) spin. The Black ellipses show the cross-sections of the nodal-surfaces formed by opposite spins.