Abstract
We study the occurrence of symmetry-enforced topological band crossings in tetragonal crystals with strong spin-orbit coupling. 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 two Weyl points in the entire Brillouin zone. This simplifies 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 Ba$_5$In$_4$Bi$_5$ and NaSn$_5$ exhibit twofold and fourfold Weyl nodal lines, respectively, which cross the Fermi energy. Hf$_3$Sb and Cs$_2$Tl$_3$ have band pairs with few number of Weyl points near the Fermi energy. Furthermore, we show that Ba$_3$Sn$_2$ has Weyl points with an accordion dispersion and topological nodal planes, while AuBr and Tl$_4$PbSe$_3$ 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.
Highlights
Topological semimetals exhibit protected band crossings near the Fermi energy, which carry nonzero topological charges [1,2,3,4,5,6,7,8]
We uncovered a rich variety of topological band crossings, which arise due to the intricate interplay of symmetry and topology (Tables I and II)
These Weyl points come in multiple copies that are related by symmetry
Summary
Topological semimetals exhibit protected band crossings near the Fermi energy, which carry nonzero topological charges [1,2,3,4,5,6,7,8]. Over the last few years it was shown that topological band crossings lead to a number of interesting phenomena, such as, unusual magnetotransport [10], intrinsic anomalous Hall effects [11], large thermopower [12], exotic surface states [13,14,15,16,17,18,19], and various responses related to quantum anomalies [20,21,22,23] Due to these unusual properties, topological semimetals hold great potential for novel device applications [24]. VI A). for the nodal planes, we find that they occur on the Brillouin zone (BZ) boundaries and are
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