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

Abstract: Unmovable nodal points (UNP) and lines (UNL) are band crossings which positions in the Brillouin zone are unaltered by symmetry preserving perturbations. Not only positions but also the band structure in the vicinity is determined by the little group of a wave vector and it's 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, great majority of which are unavoidable for a 2D material which belongs to certain layer groups. These include Weyl and Dirac nodal lines, dispersions with quadratic or cubic splitting, anisotropic Weyl and Dirac cones which orientation can be varied by e.g. strain etc. We indicated qusiparticles 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 or for fitting of experimentally (via e.g. ARPES) and numerically obtained electronic band structures as well as for deeper theoretical investigations.