# Charge density wave induced gapped nodal line

## TL;DR

This paper explores how charge density wave order can induce a gap in topological nodal-line materials, explaining recent experimental findings through a theoretical Ginzburg-Landau framework.

## Contribution

It introduces a theoretical model showing how CDW order affects nodal-line states, revealing conditions under which gaps open or nodal lines vanish.

## Key findings

- CDW order can open a gap at the Fermi energy while preserving the nodal line crossing.
- The nodal line can disappear as the Fermi level approaches it when the CDW vector approaches zero.
- Experimental observations are explained by the interplay between CDW order and symmetry breaking.

## Abstract

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.