Unified understanding of symmetry indicators for all internal symmetry classes

Ono, Shin-ichi; Watanabe, Haruki

doi:10.1103/physrevb.98.115150

Cited by 96 publications

(75 citation statements)

References 43 publications

(76 reference statements)

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“…Another important generalization is to extend the theory to cover the other ten-fold way classes [48]. This was initiated in [127], and the case most relevant for topological superconductors was discussed in [128], which also introduced a notion of weak pairing assumption that is particularly suitable for the diagnosis of topological superconductors using the normalstate symmetry representations. While particle-hole symmetry was considered in analyzing the physical meaning of the symmetry indicators in [127,128], it was not incorporated into the definition of trivial states in these early studies.…”

Section: Discussionmentioning

confidence: 99%

Symmetry indicators of band topology

2020

J. Phys.: Condens. Matter

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Topological materials are quantum materials with nontrivial groundstate entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase unconventional properties like robust anomalous surface states and quantized physical responses. The intense research efforts in understanding topological materials result in a modernized perspective on the decades-old theory of symmetry representations in electronic band structures, and inspire the development of general theories that enable the efficient diagnosis of topological materials using only symmetry data. One example is the theory of symmetry indicators of band topology, which is the focus of this topical review. We will aim at providing a pedagogical introduction to the key concepts and constructions in the theory, alongside with a brief summary of the latest development.

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Section: Discussionmentioning

confidence: 99%

Symmetry indicators of band topology

2020

J. Phys.: Condens. Matter

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“…Interestingly, some combinations of {n − (Γ j )} cannot be realized in atomic insulators. The following four numbers, calculated from n − (Γ j ), are indicators which specify whether the combinations of {n − (Γ j )} can be realized in an atomic insulator or not [48][49][50] :…”

Section: Bulk-hinge Correspondence In 3d Class Amentioning

confidence: 99%

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

Takahashi

Tanaka

Murakami

2020

Phys. Rev. Research

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We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D Z2 topological insulator. We prove it by considering a process of cutting the three-dimensional inversion-symmetric HOTI along a plane, and study the spectral flow in the cutting process. We show that the Z4 indicators, which characterize three-dimensional inversion-symmetric HOTIs in classes A and AII, are directly related to the Z2 indicators for the corresponding two-dimensional slabs with inversion symmetry, i.e. the Chern number parity and the Z2 topological invariant, for classes A and AII respectively. The existence of the gapless hinge states is understood from the conventional bulk-edge correspondence between the slab system and its edge states. Moreover, we also show that the spectral-flow analysis leads to another proof of the bulk-edge correspondence in one-and two-dimensional inversionsymmetric insulators. arXiv:1910.08290v1 [cond-mat.mes-hall]

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“…For three-dimensional (3D) insulators with T symmetry , the quantized θ term is related to Z 2 invariant directly. For the centrosymmetry insulators (breaking T symmetry), it can be reduced to a parity-based invariant, Z 4 = 0, 2 (Note that Z 4 = 1, 3 corresponds to a semimetal with Weyl nodes), which is defined as: [4][5][6]…”

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confidence: 99%

Higher-Order Topology of the Axion Insulator EuIn2As2

et al. 2019

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Based on first-principles calculations and symmetry analysis, we propose that EuIn2As2 is a long awaited axion insulator with antiferromagnetic (AFM) long range order. Characterized by the parity-based invariant Z4 = 2, the topological magneto-electric effect is quantized with θ = π in the bulk, with a band gap as large as 0.1 eV. When the staggered magnetic moment of the AFM phase is along a/b-axis, it's also a TCI phase. Gapless surface states emerge on (100), (010) and (001) surfaces, protected by mirror symmetries (nonzero mirror Chern numbers). When the magnetic moment is along c-axis, the (100) and (001) surfaces are gapped. As a consequence of a high-order topological insulator with Z4 = 2, the one-dimensional (1D) chiral state can exist on the hinge between those gapped surfaces. We have calculated both the topological surface states and hinge state in different phases of the system, respectively, which can be detected by ARPES or STM experiments.

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Unified understanding of symmetry indicators for all internal symmetry classes

Cited by 96 publications

References 43 publications

Symmetry indicators of band topology

Symmetry indicators of band topology

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

Higher-Order Topology of the Axion Insulator EuIn2As2

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