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 $\mathbf{Q}$ goes to zero. Exactly at $\mathbf{Q}=0$, the order parameter explicitly breaks the glide symmetry protecting the nodal line, which allows a gap to open. Yet, for small but finite $\mathbf{Q}$, 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.

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• Charge density waves
• Nodal-line semimetals
• Square lattice
• Landau-Ginzburg theory