Fig. 3: Band crossings and the Kramers nodal line (KNL).

a E(k_z) bands at k_x = 0.59 Å⁻¹ without (w/o) spin-orbit coupling (SOC) for the 7f structure. The irreducible representations are shown. The vertical dashed line represents the k_z point on Γ₂X₂ i.e., the Σ line in the 2^nd BZ (see Fig. 1d). Zoomed colored rectangles of a show the bands around b L, c R, d T, and e B. Comparison of ARPES and DFT for f R at k_z = 0.229 Å⁻¹and g L at k_z = 0.196 Å⁻¹. The positions of these crossings obtained from DFT (orange and blue filled circles for R and L, respectively) are superimposed. The dashed orange and blue curves serve as guide to the eye. h A schematic representation of the gapless L and R crossings in the E-k_z-k_x space (red dashed lines) and their projection on the k_x-k_z plane showing the spinless nodal lines (thick red lines on both sides of the Σ line). i–m Same as a–e except that the calculations are performed with SOC. n E(k_x) ARPES intensity plot at k_z = 0.204 Å⁻¹ (dashed red and black curves serve as guide to the eye) compared with the positions of the crossings from DFT for T (red, light red circles) and B (black, gray circles). o A schematic representation of the four crossings (green dashed lines) related to the upper and lower branches of T and B. The KNL appears along the Σ line and is denoted by a green thick line on the k_x-k_z plane.