From triple-point materials to multiband nodal links

Lenggenhager, Patrick M.; Liu, Xiaoxiong; Tsirkin, Stepan S.; Neupert, Titus; Bzdušek, Tomáš

doi:10.1103/physrevb.103.l121101

Cited by 35 publications

(51 citation statements)

References 79 publications

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“…10 to partial frames. We note in passing that while the band inversion in group 1 at Γ is mediated by a tripledegenerate point with a frame charge of q = −1 15,70,71 , the band inversion at Γ between group 2 and 3 is mediated by a quadrupledegenerate point with a total frame charge q = (−1)*(−1) = +1. Even though the frame charge of the quadruple-degenerate node is trivial, because of the crystalline symmetries it must be formed by the superposition of two quadratic nodes, each with a nonzero Edge states.…”

Section: Resultsmentioning

confidence: 86%

Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

et al. 2022

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Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that the band inversion processes at the Γ point can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of the band inversion accompanied by the braiding process.

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Section: Resultsmentioning

confidence: 86%

Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

et al. 2022

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“…Here, we describe the full derivation of the classification result shown in Ref. 50 and extend it to include TPs in spinless systems without PT symmetry and in non-symmorphic space groups. The result is a complete classification of TPs in spinless systems for all magnetic space groups according to the NL structure appearing in the vicinity of the TPs.…”

Section: Introductionmentioning

confidence: 97%

“…In Ref. 50 we have classified all possible TPs in a subset of spinless systems, namely those in systems with space-time-inversion (PT ) symmetry and symmorphic space group, according to a similar scheme as Ref. 29, and we revealed valuable connections of such TPs to non-Abelian band topology, monopole charges, and NL links [50,[55][56][57].…”

Section: Introductionmentioning

confidence: 99%

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

Lenggenhager¹,

Liu²,

Neupert³

et al. 2022

Preprint

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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 1D and a 2D irreducible corepresentation (ICR) of the little co-group. The result is a complete classification of such TPs in all magnetic space groups, including the non-symmorphic 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 co-group 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 rotation 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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“…A classic example is the quaternion group with , which has been used to classify the topological line defects in biaxial nematic liquid crystals 14 . Very recently, non-Abelian groups have been used to describe the admissible nodal line configurations 12 , 15 , 16 , Dirac/Weyl point braiding 13 , 17 , 18 , and intriguing triple nodal points 19 – 21 in PT (inversion and time-reversal) symmetric systems. When more bands are involved, richer non-Abelian topological charges emerge 9 .…”

Section: Introductionmentioning

confidence: 99%

Four-band non-Abelian topological insulator and its experimental realization

et al. 2021

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Very recently, increasing attention has been focused on non-Abelian topological charges, e.g., the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple entangled bulk bandgaps and support nontrivial edge states that manifest the non-Abelian topological features. Furthermore, a system with an even or odd number of bands will exhibit a significant difference in non-Abelian topological classification. To date, there has been scant research investigating even-band non-Abelian topological insulators. Here, we both theoretically explore and experimentally realize a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference in the four-dimensional (4D) rotation sense on the stereographically projected Clifford tori. We show the evolution of the bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way towards other even-band systems.

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From triple-point materials to multiband nodal links

Cited by 35 publications

References 79 publications

Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

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

Four-band non-Abelian topological insulator and its experimental realization

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