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We study the occurrence of symmetry-enforced topological band crossings intetragonal crystals with strong spin-orbit coupling. By computing the momentumdependence of the symmetry eigenvalues and the global band topology in theentire Brillouin zone, we determine all symmetry-enforced band crossings intetragonal space groups. In particular, we classify all Dirac and Weyldegeneracies on points, lines, and planes, and find a rich variety oftopological degeneracies. This includes, among others, double Weyl points,fourfold-double Weyl points, fourfold-quadruple Weyl points, Weyl and Diracnodal lines, as well as topological nodal planes. For the space groups withsymmetry-enforced Weyl points, we determine the minimal number of Weyl pointsfor a given band pair and, remarkably, find that materials in space groups 119and 120 can have band pairs with only two Weyl points in the entire Brillouinzone. This simplifies the topological responses, which would be useful fordevice applications. Using the classification of symmetry-enforced bandcrossings, we perform an extensive database search for candidate materials withtetragonal space groups. Notably, we find that Ba$_5$In$_4$Bi$_5$ and NaSn$_5$exhibit twofold and fourfold Weyl nodal lines, respectively, which cross theFermi energy. Hf$_3$Sb and Cs$_2$Tl$_3$ have band pairs with few number of Weylpoints near the Fermi energy. Furthermore, we show that Ba$_3$Sn$_2$ has Weylpoints with an accordion dispersion and topological nodal planes, while AuBrand Tl$_4$PbSe$_3$ possess Dirac points with hourglass dispersions. For each ofthese candidate materials we present the ab-initio band structures and discusspossible experimental signatures of the nontrivial band topology.

Symmetry-enforced band crossings in tetragonal materials: Dirac and Weyl degeneracies on points, lines, and planes