# Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials

## TL;DR

This paper systematically identifies all movable nodal lines passing through high-symmetry points in 2D materials' Brillouin zones, considering various symmetries and spin-orbit effects, with implications for material design.

## Contribution

It provides a comprehensive classification of movable nodal lines through high-symmetry points in 2D materials, including effects of spin-orbit coupling across all layer groups.

## Key findings

- Identified all movable nodal lines passing through high-symmetry points.
- Classified nodal lines based on symmetry and spin-orbit effects.
- Found that certain layer groups necessarily host Dirac and Weyl nodal lines.

## Abstract

In two-dimensional materials electronic band contacts often give non-trivial contribution to materials topological properties. Besides band contacts at high-symmetry points (HSP) in the Brillouin zone (BZ), like those in graphene, there are nodal lines which form various patterns in the reciprocal space. In this paper we have found all movable nodal lines, which shape depends on the model, that pass through HSPs in the presence of time-reversal symmetry. Cases with and without spin-orbit coupling are included by studying all eighty layer groups and their double extensions. Eight single and six double groups, including three symmorphic, necessarily host Dirac and Weyl nodal lines that extend through the whole BZ, respectively. Our research might be of interest in designing new materials with interesting physical properties.