Symmetry-Enforced Band Crossings In Tetragonal Materials: Dirac And Weyl Degeneracies On Points, Lines, And Planes

We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling and time-reversal symmetry. By computing the momentum dependence of the symmetry eigenvalues and the global band topology in the entire Brillouin zone, we determine all symmetry-enforced band crossings in tetragonal space groups. In particular, we classify all Dirac and Weyl degeneracies on points, lines, and planes, and find a rich variety of topological degeneracies. This includes, among others, double Weyl points, fourfold double Weyl points, fourfold quadruple Weyl points, Weyl and Dirac nodal lines, as well as topological nodal planes. For the space groups with symmetry-enforced Weyl points, we determine the minimal number of Weyl points for a given band pair and, remarkably, find that materials in space groups 119 and 120 can have band pairs with only twoWeyl points in the entire Brillouin zone. This simplifies the contribution of the Weyl points to the topological responses, which would be useful for device applications. Using the classification of symmetry-enforced band crossings, we perform an extensive database search for candidate materials with tetragonal space groups. Notably, we find that Ba5In4Bi5 and NaSn5 exhibit twofold and fourfold Weyl nodal lines, respectively, which cross the Fermi energy. Hf3Sb and Cs2Tl3 have band pairs with few number of Weyl points near the Fermi energy. Furthermore, we show that Ba3Sn2 has Weyl points with an accordion dispersion and topological nodal planes, while AuBr and Tl4PbSe3 possess Dirac points with hourglass dispersions. For each of these candidate materials we present the ab initio band structures and discuss possible experimental signatures of the nontrivial band topology.