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Register a new userSymmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines
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Nonsymmoprhic symmetries, such as screw rotations or glide reflections, can enforce band crossings within high-symmetry lines or planes of the Brillouin zone. When these band degeneracies are close to the Fermi energy, they can give rise to a number of unusual phenomena: e.g., anomalous magnetoelectric responses, transverse Hall currents, and exotic surface states. In this paper, we present a comprehensive classification of such nonsymmorphic band crossings in trigonal materials with strong spin-orbit coupling. We find that in trigonal systems there are two different types of nonsymmorphic band degeneracies: (i) Weyl points protected by screw rotations with an accordion-like dispersion, and (ii) Weyl nodal lines protected by glide reflections. We report a number of existing materials, where these band crossings are realized near the Fermi energy. This includes Cu2SrSnS4 and elemental tellurium (Te), which exhibit accordion Weyl points; and the tellurium-silicon clathrate Te16Si38, which shows Weyl nodal lines. The ab-initio band structures and surface states of these materials are studied in detail, and implications for experiments are briefly discussed.
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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.
We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in a simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of the space groups 56, 61, and 62 enforce nontrivial weak $mathbb{Z}_2$ topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr$_2$Bi$_3$ and Ir$_2$Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial $mathbb{Z}_2$ invariant, CuIrB possesses nodal chains near the Fermi energy, Pd$_7$Se$_4$ and Ag$_2$Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples we compute the ab-initio band structures, discuss their topologies, and for some cases also calculate the surface states.
The realization of Dirac and Weyl physics in solids has made topological materials one of the main focuses of condensed matter physics. Recently, the topic of topological nodal line semimetals, materials in which Dirac or Weyl-like crossings along special lines in momentum space create either a closed ring or line of degeneracies, rather than discrete points, has become a hot topic in topological quantum matter. Here we review the experimentally confirmed and theoretically predicted topological nodal line semimetals, focusing in particular on the symmetry protection mechanisms of the nodal lines in various materials. Three different mechanisms: a combination of inversion and time-reversal symmetry, mirror reflection symmetry, and non-symmorphic symmetry, and their robustness under the effect of spin orbit coupling are discussed. We also present a new Weyl nodal line material, the Te-square net compound KCu$_2$EuTe$_4$, which has several Weyl nodal lines including one extremely close to the Fermi level ($<$30 meV below E$_F$). Finally, we discuss potential experimental signatures for observing exotic properties of nodal line physics.
Topological phonons in crystalline materials have been attracting great interest. However, most cases studied so far are direct generalizations of the topological states from electronic systems. Here, we reveal a novel class of topological phonons -- the symmetry-enforced nodal-chain phonons, which manifest features unique for phononic systems. We show that with $D_{2d}$ little co-group at a non-time-reversal-invariant-momentum point, the phononic nodal chain is guaranteed to exist owing to the vector basis symmetry of phonons, which is a unique character distinct from electronic and other systems. Combined with the spinless character, this makes the proposed nodal-chain phonons enforced by symmorphic crystal symmetries. We further screen all 230 space groups, and find five candidate groups. Interestingly, the nodal chains in these five groups exhibit two different patterns: for tetragonal systems, they are one-dimensional along the fourfold axis; for cubic systems, they form a three-dimensional network structure. Based on first-principles calculations, we identify K$_{2}$O as a realistic material hosting almost ideal nodal-chain phonons. We show that the effect of LO-TO splitting, another unique feature for phonons, helps to expose the nodal-chain phonons in K$_{2}$O in a large energy window. In addition, all the five candidate groups have spacetime inversion symmetry, so the nodal chains also feature a quantized $pi$ Berry phase. This leads to drumhead surface phonon modes that must exist on multiple surfaces of a sample.
Two-dimensional (2D) materials have attracted great attention and spurred rapid development in both fundamental research and device applications. The search for exotic physical properties, such as magnetic and topological order, in 2D materials could enable the realization of novel quantum devices and is therefore at the forefront of materials science. Here, we report the discovery of two-fold degenerate Weyl nodal lines in a 2D ferromagnetic material, a single-layer gadolinium-silver compound, based on combined angle-resolved photoemission spectroscopy measurements and theoretical calculations. These Weyl nodal lines are symmetry protected and thus robust against external perturbations. The coexistence of magnetic and topological order in a 2D material is likely to inform ongoing efforts to devise and realize novel nanospintronic devices.
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