Nodal Lines in Noncentrosymmetric Crystals

The spin-orbit coupling (SOC) causes spin-splitting of electronic bands when there is no inversion center in the point group of the system. Different types of nodal structures (e.g., points and lines) exist in systems with different space groups. In addition to degeneracies enforced by the crystal symmetries, accidental degeneracies can also exist. In this study, we build minimal tight-binding models and elucidate the evolution of nodal line structures under different types of SOC classified by the inversion-odd irreducible representations of the point group. In particular, we show that a magnetic field can lead to transitions from nodal lines to nodal rings to nodeless structures in spin-orbit coupled systems, in ways reminiscent of altermagnets.