Structure and topology of band structures in the 1651 magnetic space groups

Watanabe, Haruki; Po, Hoi Chun; Vishwanath, Ashvin

doi:10.1126/sciadv.aat8685

Cited by 268 publications

(223 citation statements)

References 76 publications

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“…Lastly, we note that the theory of symmetry indicators has also been extended to other symmetry setting. As briefly reviewed in section 7.4, the symmetry indicator groups appropriate for magnetic materials have already been exhaustively computed in [70], although a comprehensive analysis of their relation to the physical phases of topological materials remains an open question. Another important generalization is to extend the theory to cover the other ten-fold way classes [48].…”

Section: Discussionmentioning

confidence: 99%

“…The band topology of weakly correlated materials with frozen magnetic orders can be diagnosed using the same methods described in section 6.2. However, unlike the time-reversal symmetric cases, the physical interpretation of the symmetry indicators in the magnetic case remains an open problem, with the existing results only covering certain specific cases [59,60,61,70,123]. In particular, some nontrivial indicators correspond to topological nodal (semi-)metal whereas some others correspond to TIs and TCIs, as was highlighted in section 7.2 for materials with only lattice translation and inversion symmetry [59,60].…”

Section: Magnetically Ordered Materialsmentioning

confidence: 99%

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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%

Section: Magnetically Ordered Materialsmentioning

confidence: 99%

Symmetry indicators of band topology

2020

J. Phys.: Condens. Matter

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“…Here there has been dramatic progress in recent years, with new approaches having emerged based on topological band theory 7,8 and symmetry indicators, 9 most recently including magnetic groups. 10 These have allowed for impressive progress in clarifying the full variety of possible topological states of crystalline insulators.…”

Section: Introductionmentioning

confidence: 99%

Axion coupling in the hybrid Wannier representation

2020

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Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that do not ("axion-even" or "trivial"). For time-reversal or inversion symmetries, the resulting topological state is usually denoted as a "strong topological insulator" or an "axion insulator" respectively, but many other symmetries can also protect this "axion Z2" index. Topological states are often insightfully characterized by choosing one crystallographic direction of interest, and inspecting the hybrid Wannier (or equivalently, the non-Abelian Wilson-loop) band structure, considered as a function of the two-dimensional Brillouin zone in the orthogonal directions. Here, we systematically classify the axion-quantizing symmetries, and explore the implications of such symmetries on the Wannier band structure. Conversely, we clarify the conditions under which the axion Z2 index can be deduced from the Wannier band structure. In particular, we identify cases in which a counting of Dirac touchings between Wannier bands, or a calculation of the Chern number of certain Wannier bands, or both, allows for a direct determination of the axion Z2 index. We also discuss when such symmetries impose a "flow" on the Wannier bands, such that they are always glued to higher and lower bands by degeneracies somewhere in the projected Brillouin zone, and the related question of when the corresponding surfaces can remain gapped, thus exhibiting a half-quantized surface anomalous Hall conductivity. Our formal arguments are confirmed and illustrated in the context of tight-binding models for several paradigmatic axion-odd symmetries including time reversal, inversion, simple mirror, and glide mirror symmetries.

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“…In this work, by applying the filling-constraint method [52][53][54], we find serveral magnetic topological metals: XFe 4 Ge 2 (X = Y, Lu) and Mn 3 Pt. We display detailed analysis for the topological features of XFe 4 Ge 2 , where Dirac points are located at S point near the Fermi energy.…”

Section: Introductionmentioning

confidence: 98%

XFe4Ge2(X=Y,Lu) and
Wang
¹
,
Tang
²
,
Po
³

et al. 2020
Phys. Rev. B
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Magnetism, coupled with nontrivial band topology, can bring about many interesting and exotic phenomena, so that magnetic topological materials have attracted persistent research interest. However, compared with non-magnetic topological materials (TMs), the magnetic TMs are less studied, since their magnetic structures and topological phase transitions are usually complex and the firstprinciples predictions are usually sensitive on the effect of Coulomb interaction. In this work, we present a comprehensive investigation of XFe4Ge2 (X = Y, Lu) and Mn3Pt, and find these materials to be filling-enforced magnetic topological metals. Our first-principles calculations show that XFe4Ge2 (X = Y, Lu) host Dirac points near the Fermi level at high symmetry point S. These Dirac points are protected by P T symmetry (P and T are inversion and time-reversal transformations, respectively) and a 2-fold screw rotation symmetry. Moreover, through breaking P T symmetry, the Dirac points would split into Weyl nodes. Mn3Pt is found to host 4-fold degenerate band crossings in the whole high symmetry path of A-Z. We also utilize the GGA + U scheme to take into account the effect of Coulomb repulsion and find that the filling-enforced topological properties are naturally insensitive on U .

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Structure and topology of band structures in the 1651 magnetic space groups

Abstract: Topological properties of band structures in magnetic materials are systematically studied using symmetry representations.

Cited by 268 publications

References 76 publications

Symmetry indicators of band topology

Symmetry indicators of band topology

Axion coupling in the hybrid Wannier representation

XFe4Ge2(X=Y,Lu) and
Wang
¹
,
Tang
²
,
Po
³

et al. 2020
Phys. Rev. B
Self Cite
28
0
42
0
View full text Add to dashboard Cite

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Structure and topology of band structures in the 1651 magnetic space groups

Abstract: Topological properties of band structures in magnetic materials are systematically studied using symmetry representations.

Cited by 268 publications

References 76 publications

Symmetry indicators of band topology

Symmetry indicators of band topology

Axion coupling in the hybrid Wannier representation

XFe4Ge2(X=Y,Lu) and Wang1, Tang2, Po3 et al. 2020Phys. Rev. BSelf Cite280420View full textAdd to dashboardCite

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XFe4Ge2(X=Y,Lu) and
Wang
¹
,
Tang
²
,
Po
³

et al. 2020
Phys. Rev. B
Self Cite
28
0
42
0
View full text Add to dashboard Cite