Charge density wave induced gapped nodal line

We investigate the interplay between charge density wave (CDW) order and topological nodal-line states in square-net materials. Our Ginzburg-Landau theory predicts a CDW instability that generically opens a gap at the Fermi energy while preserving the nodal-line crossing. However, as the Fermi level approaches the nodal line, the density of states at the nodal line decreases, eventually disappearing as the CDW vector Q goes to zero. Exactly at Q = 0, the order parameter explicitly breaks the glide symmetry protecting the nodal line, which allows a gap to open. Yet, for small but finite Q, the nodal line may vanish within experimental resolution even when the glide symmetry is preserved. Our results provide a consistent explanation for recent experimental observations.