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

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.

arXiv comment31 pages, 17 figures

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• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Semi-Dirac and Weyl Fermions in Transition Metal Oxides
• Superconductivity of anomalous pseudospin
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Altermagnetic Instabilities from Quantum Geometry
• Gapped nodal planes drive a large topological Nernst effect in a chiral lattice antiferromagnet
• Fundamental laws of chiral band crossings: local constraints, global constraints, and topological phase diagrams
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Two-dimensional half Chern-Weyl semimetal with multiple screw axes
• Upper bound of a band complex
• Linear Magnetoresistance and Type-I Superconductivity in $\beta$-IrSn${}_4$
• Electronic Structure of the Bond Disproportionated Bismuthate Ag${}_2$BiO${}_3$
• Electronic structures near unmovable nodal points and lines in two-dimensional materials
• Electronic switching of topology in LaSbTe
• Fidelity and variability in the interlayer electronic structure of the kagome superconductor CsV3Sb5
• Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials
• Topological charge distributions of an interacting two-spin system
• Intrinsic defect intolerance in the ultra-pure metal PtSn${}_4$
• Local symmetry groups for arbitrary wavevectors
• Tunable Octdong and Spindle-Torus Fermi Surfaces in Kramers Nodal Line Metals
• Low temperature phase of AuSn${}_4$ induced by the van der Waals interactions
• Structural characterization of the candidate Weyl semimetal CeGaGe
• Observation of Quadratic (Charge-2) Weyl Point Splitting in Near-Infrared Photonic Crystals
• Essentially degenerate hidden nodal lines in two-dimensional magnetic layer groups
• Weak ${\mathbb{Z}}_2$ Supertopology
• Signatures of symmetry-stabilized Dirac fermions in correlated oxide CaNbO3 thin films