Radial Spin Texture of the Weyl Fermions in Chiral Tellurium

Gatti, G.; Gosálbez-Martínez, Daniel; Tsirkin, Stepan S.; Fanciulli, Mauro; Puppin, Michele; Polishchuk, S.; Moser, Simon; Testa, Luc; Martino, Edoardo; Roth, Silvan; Bugnon, Philippe; Moreschini, Luca; Bostwick, Aaron; Rotenberg, Eli; Santo, Giovanni Di; Petaccia, L.; Vobornik, I.; Fujii, Jun; Wong, Joeson; Jariwala, Deep; Atwater, Harry A.; Rønnow, Henrik M.; Chergui, Majed; Yazyev, Oleg V.; Grioni, M.; Crepaldi, Alberto

doi:10.1103/physrevlett.125.216402

Cited by 72 publications

(46 citation statements)

References 41 publications

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“…Different shapes of spin texture (ST) were observed, including radial texture 𝑆 !" ∥ 𝑘 (known as Weyl ST) [5][6][7], or the tangential texture 𝑆 !" ⊥ 𝑘 (known as 'Rashba ST') [8][9][10], or the tangential--radial texture (known as 'Dresselhaus ST') [11,12].…”

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Different shapes of spin textures as a journey through the Brillouin zone

et al. 2021

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Crystallographic space group symmetry (CPGS) such as polar and nonpolar crystal classes has long been known to classify compounds that have spin--orbit--induced spin splitting such as Rashba and Dresselhaus compounds, respectively. However, the enabling symmetries underlying the spin texture prototypes ---the relationship between the expectation value of spin operator 𝑆 !" in Bloch state 𝑢(𝑛, 𝑘) and the wavevector 𝑘 - are instead specific rotations and reflection symmetries in the wavevector point group symmetry rather than the presence or absence of polar field in the global crystallographic space group. Relativistic band structures calculations demonstrate how compounds judged by their macroscopic CPGS to be typical Dresselhaus (GaAs) or Rashba (GeTe) or Wyle (Tellurium) compounds, manifest both Rashba and Dresselhaus spin textures, respectively at different wavevector chiralities and polarities.

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Different shapes of spin textures as a journey through the Brillouin zone

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“…Previously, we have applied this strategy to hexagonal, trigonal, and tetragonal crystals [16][17][18]. These investigations have uncovered, among other things, the accordion states in trigonal Te [36], and identified ZrIrSn and NaSn 5 as nodal line materials with twofold and fourfold Weyl lines, respectively [16,18]. In this paper, we continue this classification program by investigating symmetry-enforced band crossings in orthorhombic crystals.…”

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confidence: 94%

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

Leonhardt,

Hirschmann,

Heinsdorf

et al. 2021

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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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“…Depending on whether or not the little groups of the k points of the enforced nodal degeneracies (as well as the full space group) contain rotoinversion symmetries, the ESFD semimetals identified in this section may further be classified as topologically chiral or achiral [120,121]. ESFD phases in structurally chiral crystals have in particular been highlighted for hosting monopole-like spin textures [121,187], exhibiting photoresponse signatures of topological chirality [122,[188][189][190][191], and as possible venues for realizing topological superconductivity [192][193][194].…”

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All Topological Bands of All Stoichiometric Materials

Vergniory,

Wieder,

Elcoro

et al. 2021

Preprint

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The recently introduced theories of Topological Quantum Chemistry and Symmetry-Based Indicators (SIs) have facilitated the discovery of novel stable topological phases of matter and largescale searches for materials with experimentally accessible topological properties at the Fermi energy (EF ). In this work, we have completed the first catalog of stable and fragile topology in all of the bands both at and away from EF in the Inorganic Crystal Structure Database (ICSD), which we have made accessible through a substantial upgrade of Topological Materials Database (https://www.topologicalquantumchemistry.com/). We have computed the electronic structure, topological class, and stable and fragile SIs of all bands in the 96,196 processable ICSD entries with stoichiometric chemical formulas in the presence and absence of spin-orbit coupling, which we have grouped into 38,298 unique materials by common chemical formulas, crystal structures [space groups (SGs)], and topology at EF . Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and a doubling of the number of materials accessible in previous topological material catalogs. Through our calculations, we discover the existence of novel classes of topological materials, including enforced topological semimetals with energetically isolated fragile bands at EF , repeat-topological (RTopo) materials with stable topological insulating gaps at and just below EF , and supertopological (STopo) materials in which every energetically isolated set of bands above the core shell is stable topological. Our findings recontextualize several previous experimental investigations of topological materials. We find that the transition-metal chalcogenides Ta2NiSe5 in SG 15 (C/2c) and Ta2NiSe7 in SG 12 (C2/m) -respectively previously highlighted for hosting exciton-insulator and charge-density-wave phases -are 3D topological insulators (TIs) in their normal states. Additionally, we find that the higher-order TI rhombohedral bismuth in SG 166 (R 3m) and the indirect-gap TI Bi2Mg3 in SG 164 (P 3m1) are both RTopo and STopo materials. Previous ARPES investigations of Bi2Mg3 have demonstrated the presence of "surface resonance bands" below EF -in this work, we discover that the surface resonance bands are in fact RTopo Dirac-cone surface states. We present detailed statistics for our computations revealing that 52.65% of all materials are topological at EF , roughly 2/3 of bands across all materials exhibit symmetry-indicated stable topology, and that, shockingly, 87.99% of all materials contain at least one stable or fragile (crystalline) topological band in their spectrum (though potentially far from EF ). Our findings motivate the formulation of a new periodic table of chemical compounds based on the ubiquity of nontrivial electronic band topology in solid-state materials.

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Radial Spin Texture of the Weyl Fermions in Chiral Tellurium

Cited by 72 publications

References 41 publications

Different shapes of spin textures as a journey through the Brillouin zone

Different shapes of spin textures as a journey through the Brillouin zone

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

All Topological Bands of All Stoichiometric Materials

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