Phononic Helical Nodal Lines with $\mathcal{P}\mathcal{T}$ Protection in MoB${}_2$

Abstract

While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such a phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal ($\mathcal{P}\mathcal{T}$) symmetry protected helical nodal lines in the phonon spectrum of MoB${}_2$. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

References in corpus (26)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• WannierTools: An open-source software package for novel topological materials
• Topological quantum chemistry
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• The (High Quality) Topological Materials In The World
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• Catalogue of Topological Electronic Materials
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topological nodal line semimetals
• Dirac Semimetals in Two Dimensions
• Topological classification of crystalline insulators through band structure combinatorics
• Double-Weyl phonons in transition-metal monosilicides
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Many-body Effects in Angle-resolved Photoemission: Quasiparticle Energy and Lifetime of a Mo(110) Surface State
• Quantitative mappings between symmetry and topology in solids
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Observation of Double Weyl Phonons in Parity-Breaking FeSi
• Topological phonons and Weyl lines in 3 dimensions
• Dirac and nodal line magnons in three-dimensional antiferromagnets
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• Topological spin excitations observed in a three-dimensional antiferromagnet
• Incommensurate phonon anomaly and the nature of charge density waves in cuprates
• Nanoscale Surface Dynamics of Bi${}_2$Te${}_3$(111): Observation of a Prominent Surface Acoustic Wave and the Role of van der Waals Interactions

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• Observation of a Chiral Wave Function in Twofold Degenerate Quadruple Weyl System BaPtGe
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• Diboride compounds doped with transition metals$\unicode{x2013}$a route to superconductivity through structure stabilization as well as defects
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Symmetry-enforced planar nodal chain phonons in non-symmorphic materials
• Chiral phonons in binary compounds $A$Bi ($A$ = K, Rb, Cs) with P2${}_1$/c structure
• $T_3$Pb${}_{2}C{h}_2$ ($T$=Pd,Pt and $Ch$=S,Se) with transition metal kagome net: Dynamical properties, phonon nodal line, phonon surface states, and chiral phonons
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• Chiral Topological Phononic Quasiparticles in Enantiomeric Crystals SrSi${}_2$ and BaSi${}_2$
• Multiple types of unconventional quasiparticles in the chiral crystal CsBe${}_2$F${}_5$
• Chiral phononic and electronic edge modes of EuPtSi
• Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
• Ferroelectrically Controlled Chirality Switching of Weyl Quasiparticles
• Three-nodal surface phonons in solid-state materials: Theory and material realization