Symmetry indicators of band topology

Po, Hoi Chun

doi:10.1088/1361-648x/ab7adb

Cited by 76 publications

(59 citation statements)

References 142 publications

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“…To this end, we take inspiration from the idea of symmetry indicators (21)(22)(23)(24) (see ref. 39 for a review), and extend those developed for Chern insulators (40). Relevant to our analysis, the latter work established, in particular, that, in 2D crystals with Cn rotational symmetry, the Chern number can be determined modulo n by multiplying rotation eigenvalues of filled states.…”

Section: Resultssupporting

confidence: 67%

Topological Weaire–Thorpe models of amorphous matter

Marsal

Varjas

Grushin

2020

Proc. Natl. Acad. Sci. U.S.A.

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Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire–Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route toward a complete classification of amorphous topological states in real space using quasilocal properties.

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Section: Resultssupporting

confidence: 67%

Topological Weaire–Thorpe models of amorphous matter

Marsal

Varjas

Grushin

2020

Proc. Natl. Acad. Sci. U.S.A.

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“…The detailed calculations for the Z 2 invariants in all six TRI planes (only four of them are distinct due to the symmetry) are presented in Supplementary Section B 63 . Furthermore, the symmetry indicators [64][65][66][67] for these compounds are computed to be Z 3m;0 ¼ 1 and Z 3m;π ¼ 0, revealing the topological nature of the SOC gap (shadowed in light blue) in Fig. 2b.…”

Section: Resultsmentioning

confidence: 97%

Topological electronic states in HfRuP family superconductors

Qian¹,

Nie²,

Yi³

et al. 2019

npj Comput Mater

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Based on the first-principles calculations and experimental measurements, we report that the hexagonal phase of ternary transition metal pnictides TT'X (T=Zr, Hf; T'=Ru; X=P, As), which are well-known noncentrosymmetric superconductors with relatively high transition temperatures, host nontrivial bulk topology. Before the superconducting phase transition, we find that HfRuP belongs to a Weyl semimetal phase with 12 pairs of type-II Weyl points, while ZrRuAs, ZrRuP and HfRuAs belong to a topological crystalline insulating phase with trivial Fu-Kane Z 2 indices but nontrivial mirror Chern numbers. High-quality single crystal samples of the noncentrosymmetric superconductors with these two different topological states have been obtained and the superconductivity is verified experimentally. The wide-range band structures of ZrRuAs have been identified by ARPES and reproduced by theoretical calculations. Combined with intrinsic superconductivity, the nontrivial topology of the normal state may generate unconventional superconductivity in both bulk and surfaces. Our findings could largely inspire the experimental searching for possible topological superconductivity in these compounds.

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“…We believe that the sum rule is related to the space-group symmetry of the entire lattice, as well as to the site symmetry of Cu 2+ . A close-knit comparison between real-and reciprocal-space pictures has led to a recent progress in the understanding of electronic band topology [29,30], where the high symmetry of Cu3TeO6 has been noted as an extreme case of interconnected bands [29]. A counterpart analysis for magnon states in the magnetic groups [20] may lead to new insights for the prediction of novel magnon systems.…”

Section: Figure 3 | Comparison Between Measured and Calculated Magnonmentioning

confidence: 99%

Topological spin excitations in a three-dimensional antiferromagnet

et al. 2018

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Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises [1-4]. While band crossing of non-trivial topological nature was first studied in three dimensions for electrons [4-10], the underlying physical idea is not restricted to fermionic excitations [11-15]. In fact, experiments have confirmed the possibility to have topological band crossing of electromagnetic waves in artificial structures [16]. Fundamental bosonic excitations in real crystals, however, have not been observed to exhibit the counterpart under ambient pressure and magnetic field, where the difficulty is in part because natural materials cannot be precisely engineered like artificial structures. Here, we use inelastic neutron scattering to reveal the presence of topological spin excitations (magnons) in a three-dimensional antiferromagnet, Cu3TeO6, which features a unique lattice of magnetic spin-1/2 Cu 2+ ions [17]. Beyond previous understanding [17,18], we find that the material's spin lattice possesses a variety of exchange interactions, with the interaction between the ninth-nearest neighbours being as strong as that between the nearest neighbours. Although theoretical analysis indicates that the presence of topological magnon band crossing is independent of model details [15], Cu3TeO6 turns out to be highly favourable for the experimental observation, as its optical magnons are spectrally sharp and intense due

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Symmetry indicators of band topology

Cited by 76 publications

References 142 publications

Topological Weaire–Thorpe models of amorphous matter

Topological Weaire–Thorpe models of amorphous matter

Topological electronic states in HfRuP family superconductors

Topological spin excitations in a three-dimensional antiferromagnet

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