Topological band crossings in hexagonal materials

Zhang, Jonathan; Chan, Yang-Hao; Chiu, Ching-Kai; Vergniory, Maia G.; Schoop, Leslie M.; Schnyder, Andreas P.

doi:10.1103/physrevmaterials.2.074201

Cited by 49 publications

(49 citation statements)

References 75 publications

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“…[50]. Using the terminology of symmorphic and nonsymmorphic symmetries, one should call n a symmorphic symmetry depending on the quasimomentum k (for Z even and n odd, sometimes also called unconventional nonsymmorphic symmetry) since it returns to the same lattice site when applied twice [107][108][109][110], whereas S n is a nonsymmorphic symmetry [111].…”

Section: Nonlocal Symmetriesmentioning

confidence: 99%

Rational boundary charge in one-dimensional systems with interaction and disorder

Pletyukhov

Kennes

Piasotski

et al. 2020

Phys. Rev. Research

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We study the boundary charge Q B of generic semi-infinite one-dimensional insulators with translational invariance and show that nonlocal symmetries (i.e., including translations) lead to rational quantizations p/q of Q B. In particular, we find that (up to an unknown integer) the quantization of Q B is given in integer units of 1 2ρ and 1 2 (ρ − 1), whereρ is the average charge per site (which is a rational number for an insulator). This is a direct generalization of the known half-integer quantization of Q B for systems with local inversion or local chiral symmetries to any rational value. Quite remarkably, this rational quantization remains valid even in the presence of short-ranged electron-electron interactions as well as static random disorder (breaking translational invariance). This striking stability can be traced back to the fact that local perturbations in insulators induce only local charge redistributions. We establish this result with complementary methods including density matrix renormalization group calculations, bosonization methods, and exact solutions for particular lattice models. Furthermore, for the special case of half-fillingρ = 1 2 , we present explicit results in single-channel and nearest-neighbor hopping models and identify Weyl semimetal physics at gap closing points. Our general framework also allows us to shed new light on the well-known rational quantization of soliton charges at domain walls.

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Section: Nonlocal Symmetriesmentioning

confidence: 99%

Rational boundary charge in one-dimensional systems with interaction and disorder

Pletyukhov

Kennes

Piasotski

et al. 2020

Phys. Rev. Research

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“…Topological materials have attracted great interest both theoretically and experimentally 1-3 since the proposal of topological insulators (TIs) in 2005. 4 Generally speaking, topological materials can be classified into gapped phases, such as TIs and topological superconductors (TSCs), 1,2 and gapless phases consisting of various topological semimetals (TSMs), such as Weyl semimetals (WSMs), Dirac semimetals(DSMs), [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] nodal-line semimetals (NLSMs), [44][45][46][47][48][49][50][51][52][53] and nodal surface semimetals (NSSMs), [54][55][56][57][58] etc. Symmetries play important roles in the classification of topological phases.…”

Section: Introductionmentioning

confidence: 99%

Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

et al. 2019

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It has recently been found that nonsymmorphic symmetries can bring many exotic band crossings. Here, based on symmetry analysis, we predict that materials with time-reversal symmetry in the space group of Pbca (No. 61) possess rich symmetry-enforced band crossings, including nodal surfaces, fourfold degenerate nodal lines and hourglass Dirac loops, which appear in triplets as ensured by the cyclic permutation symmetry. We take Pbca AgF 2 as an example in real systems and studied its band structures with ab initio calculations. Specifically, in the absence of spin-orbit coupling (SOC), besides the above-mentioned band degeneracies, this system features a nodal chain and a nodal armillary sphere penetrating the Brillouin zone (BZ). While with SOC, we find a new configuration of the hourglass Dirac loop/chain with the feature traversing the BZ, which originates from the splitting of a Dirac loop confined in the BZ. Furthermore, guided by the bulk-surface correspondence, we calculated the surface states to explore these bulk nodal phenomena. The evolution of these interesting nodal phenomena traversing the BZ under two specific uniaxial strains is also discussed.npj Computational Materials (2019) 5:53 ; https://doi.

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“…materials [38], there exist no band crossings protected by off-centered symmetries [35][36][37]. We note that our analysis takes into account the full connectivity of the bands in the entire BZ, which goes beyond the results obtained through symmetry indicators [45][46][47].…”

Section: Introductionmentioning

confidence: 96%

“…This fact allows us to construct the following strategy to discover new topological semimetals, which consists of three steps: (i) identify the space groups (SGs) whose nonsymmorphic symmetries enforce the desired band crossings, (ii) perform a database search for materials in these SGs, and (iii) compute the electronic band structure of these materials to check whether the band crossings are near the Fermi energy. Previously, we applied this strategy to discover new topological semimetals with hexagonal symmetries [38]. Here, we extend this analysis to trigonal systems.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines

Chan

Kilic

Hirschmann

et al. 2019

Phys. Rev. Materials

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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 accordionlike 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 telluriumsilicon 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. arXiv:1908.00901v1 [cond-mat.mtrl-sci]

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Topological band crossings in hexagonal materials

Cited by 49 publications

References 75 publications

Rational boundary charge in one-dimensional systems with interaction and disorder

Rational boundary charge in one-dimensional systems with interaction and disorder

Composite topological nodal lines penetrating the Brillouin zone in orthorhombic AgF2

Symmetry-enforced band crossings in trigonal materials: Accordion states and Weyl nodal lines

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