Movable but unavoidable nodal lines through high-symmetry points in 2D materials

Abstract

Abstract In 2D materials, electronic band contacts often make a non-trivial contribution to a material’s topological properties. Besides band contacts at high-symmetry points (HSPs) in the Brillouin zone (BZ), like those in graphene, there are nodal lines that form various patterns in the reciprocal space. In this paper we have found all movable nodal lines, whose 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 80 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.