Symmetry-protected nodal points and nodal lines in magnetic materials

Yang, Jian; Fang, Chen; Liu, Zheng-Xin

doi:10.1103/physrevb.103.245141

Cited by 21 publications

(10 citation statements)

References 48 publications

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“…The presented characterization of TPs applies to spinless representations in all space groups (magnetic or not, nonsymmorphic or not), and as such provides that next essential piece of information towards the growing catalog of symmetryprotected and symmetry-enforced band nodes [52,[86][87][88][89]. Nevertheless, it may be hard to find examples of electronic material which are well described by spinless band structures.…”

Section: Discussionmentioning

confidence: 99%

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

et al. 2022

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We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a one-dimensional (1D) and a two-dimensional (2D) irreducible corepresentation (ICR) of the little cogroup. The result is a complete classification of such TPs in all magnetic space groups, including the nonsymmorphic ones, according to several characteristics of the nodal-line structure at and near the TP. We show that the classification of the presently studied TPs is exhausted by 13 magnetic point groups (MPGs) that can arise as the little cogroup of a high-symmetry line and which support both 1D and 2D spinless ICRs. For 10 of the identified MPGs, the TP characteristics are uniquely determined without further information; in contrast, for the 3 MPGs containing sixfold rotational symmetry, two types of TPs are possible, depending on the choice of the crossing ICRs. The classification result for each of the 13 MPGs is illustrated with first-principles calculations of a concrete material candidate.

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Section: Discussionmentioning

confidence: 99%

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

et al. 2022

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“…( C6)]. While the discovery of magnetic topological materials is a fruitful field of ongoing study [143,144,151,170,171,264,[266][267][268][269][270], we will only focus in this work on applying the T -broken formulation of M F ν to simple tight-binding models -which are provided in Appendices D, E -as opposed to real-material magnetic topological (crystalline) insulators. However, in Appendix C 2 b, we will shortly formulate a T -symmetric extension of M F ν , which can be used to predict spin-charge separated HEND states in nonmagnetic 3D insulators.…”

Section: Ebrs Of Magnetic Layermentioning

confidence: 99%

Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators

Schindler¹,

Tsirkin²,

Neupert³

et al. 2022

Preprint

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In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find that π-flux tubes in inversion-and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states.

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“…In Ref. [45], Yang et al study band touchings in magnetic space groups that contain the product of time-reversal and inversion. Furthermore, with the aid of magnetic topological quantum chemistry [46], first-principles calculations have been performed to investigate the band touchings of magnetic compounds from the Bilbao Crystallographic Server [47].…”

Section: Introductionmentioning

confidence: 99%

Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

Knoll,

Timm

2021

Preprint

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Symmetry-protected topological semimetals are at the focus of solid-state research due to their unconventional properties, for example regarding transport. By investigating local two-band Bloch Hamiltonians in the spin-1/2 basis for the 122 magnetic point groups, we classify twofold-degenerate band touchings such as Weyl points, robust nodal lines on axes and in mirror planes, and fragile nodal lines. We find that all magnetic point groups that lack the product of inversion and timereversal symmetries can give rise to topologically non-trivial band-touching points. Hence, such nodes are the rule rather than the exception and, moreover, do not require any complicated multiband physics. Our classification is applicable to every momentum in the Brillouin zone by considering the corresponding little group and provides a powerful tool to identify magnetic and non-magnetic topological semimetals.

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Symmetry-protected nodal points and nodal lines in magnetic materials

Cited by 21 publications

References 48 publications

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators

Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles

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