Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

Shao, Ding-Fu; Wang, Huaiqiang; Chen, Tong; Lu, Pengchao; Gu, Qinyan; Sheng, L.; Xing, D. Y.; Sun, Junqiang

doi:10.1038/s41524-019-0190-3

Cited by 17 publications

(15 citation statements)

References 97 publications

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“…The compound LiBH may prove to be a valuable realization of a material, where a twofold nodal line and a nodal plane with a pinned fourfold nodal line coexist in the vicinity of the Fermi energy [70]. Other known orthorhombic realizations of movable enforced nodal lines in the vicinity of the Fermi energy include AgF 2 (SG 61) [71], Ba 2 ReO 5 (SG 62) [65], and SrIrO 3 (SG 62) [72]. Accidental nodal lines have been found for BaLi 2 Sn (SG 59) [73], BaLi 2 Si (SG 59) [74], ZrAs 2 (SG 62) [75], Ta 3 SiTe 6 and related compounds (SG 62) [76,77], as well as 3D α boron (SG 63) [78].…”

Section: Materials Examplesmentioning

confidence: 99%

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

Leonhardt,

Hirschmann,

Heinsdorf

et al. 2021

Preprint

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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 Z2 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 Sr2Bi3 and Ir2Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial Z2 invariant, CuIrB possesses nodal chains near the Fermi energy, Pd7Se4 and Ag2Se exhibit fourfold double Weyl points, the latter one even in the absence of spinorbit 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.

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Section: Materials Examplesmentioning

confidence: 99%

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

Leonhardt,

Hirschmann,

Heinsdorf

et al. 2021

Preprint

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show abstract

“…To our knowledge, a similar arrangement of bands has only been discussed in systems without spin-orbit coupling. For the cubic SG 221 three intersecting planes with joined nodal lines were considered [88,89], whereas in the orthorhombic SG 61 two intersecting nodal lines were referred to as a nodal armillary sphere [90]. These nodal lines gap out once spin-orbit is relevant, unlike the feature of SG 110 presented here.…”

Section: Intersecting Nodal Lines Of Sg 110mentioning

confidence: 99%

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

Hirschmann,

Leonhardt,

Kilic

et al. 2021

Preprint

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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 symmetryenforced 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 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.

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“…Recently, the topic of band crossings has been extensively revisited in the context of topological characterization of the electronic structure of semimetals. [5][6][7][8][9][10] It is well established that if nonsymmorphic symmetries are present in a crystalline lattice, they will enforce the crossing of electronic bands. [11][12][13][14] Dirac and/or Weyl points are formed and they are globally stable.…”

Section: Introductionmentioning

confidence: 99%

“…[11][12][13][14] Dirac and/or Weyl points are formed and they are globally stable. [5][6][7][8][9][10] The band crossing can also occur at generic k points in the Brillouin zone and is independent of the symmetry properties of the system, including the lattice symmetries and the reality of the Hamiltonian. This case is called accidental band crossings that were first discussed by Herring in 1937.…”

Section: Introductionmentioning

confidence: 99%

Electronic band crossing in sliding bilayer graphene: Tight-binding calculations and symmetry group representation analysis

Do¹

2021

Preprint

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Dirac points are found to emerge due to the crossing of bands in the electronic structure of bilayer graphene for configurations in which the alignment between two hexagonal lattices preserves the parallelism of the armchair/zigzag lines between two layers. On the base of electronic calculations using a tight-binding model for the π bands it is shown that the crossing of the energy-band dispersion curves occurs in the vicinity of the corner points of the hexagonal Brillouin zone. Group representation theory analysis confirms the emergence of such Dirac points. It is demonstrated that the band crossings at generic k points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry k points in the Brillouin zone. The presence of Dirac points governs the geometrical properties of the energy surfaces, and thus the topological structure of the Fermi energy surface and the energy spectrum.

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Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

Cited by 17 publications

References 97 publications

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery

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

Electronic band crossing in sliding bilayer graphene: Tight-binding calculations and symmetry group representation analysis

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