Electronic structures near unmovable nodal points and lines in two-dimensional materials

Abstract

Unmovable nodal points (UNPs) and lines (UNLs) are band crossings whose positions in the Brillouin zone are unaltered by symmetry preserving perturbations. Not only positions but also the band structure in their vicinity are determined by the little group of wave vectors and its irreducible (co)representations. In this paper, we give the full set of electronic dispersions near all UNPs and UNLs in non-magnetic quasi two-dimensional (2D) materials, both with and without spin–orbit coupling (SOC). Analysis of all layer gray single and double groups gives nineteen different quasiparticles, the great majority of which are unavoidable for a 2D material that belongs to a certain layer group. This includes Weyl and Dirac nodal lines, dispersions with quadratic or cubic splitting, anisotropic Weyl and Dirac cones, whose orientation can be varied by e.g. strain etc. We indicated quasiparticles that are robust to SOC. For convenience, our results are concisely presented graphically—as a map, not in a tabular, encyclopedia form. They may be of use as checkpoints and/or for fitting experimentally (via e.g. ARPES) and numerically obtained electronic band structures data, as well as for deeper theoretical investigations.