Fig. 1: The energy bands ε_c(p) and ε_v(p), Eq. (1), in the vicinity of their nodal line in the plane p_z = 0 perpendicular to the line.

The red solid and black dashed lines show the bands with and without the spin–orbit interaction, respectively. The red circles mark the minimum of ε_c(p) and the maximum of ε_v(p) in the plane. The minimal indirect gap \(2{{{\Delta }}}_{\min }=2{{\Delta }}{(1-{\tilde{a}}_{\perp }^{2})}^{1/2}\) determined by these two points is less than 2Δ, the spin–orbit gap at p = 0. Here \({p}_{1}\equiv ({a}_{x}{p}_{x}+{a}_{y}{p}_{y})/({\tilde{a}}_{\perp }{{\Delta }})\) is the dimensionless quasimomentum measured along the vector \(({\tilde{a}}_{x},{\tilde{a}}_{y})\) in the plane with the coordinates p_xv_x/Δ and p_yv_y/Δ; \({\tilde{a}}_{i}\equiv {a}_{i}/{v}_{i}\), and \({\tilde{a}}_{\perp }\equiv {({\tilde{a}}_{x}^{2}+{\tilde{a}}_{y}^{2})}^{1/2}\). The dotted line indicates the Fermi level E_F. Upper inset: The Fermi surface enclosing the nodal line (the dash-dotted line) at (E_F − ε_d)b < 0. Lower inset: The cross section (ellipse) of the Fermi surface on the plane p_z = 0. The black dashed line marks the direction along which the bands are shown in the main panel. The black asterisk and green cross mark the point p = 0 and the center of the ellipse, respectively.