Topological phonons and Weyl lines in 3 dimensions

Abstract

Topological mechanics and phononics have recently emerged as an exciting field of study. Here we introduce and study generalizations of the three-dimensional pyrochlore lattice that have topologically protected edge states and Weyl lines in their bulk phonon spectra, which lead to zero surface modes that flip from one edge to the opposite as a function of surface wavenumber.

7 pages, 7 figures

References in corpus (4)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator

Cited by in corpus (67)

• Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Dirac magnons in honeycomb ferromagnets
• Dirac and nodal line magnons in three-dimensional antiferromagnets
• Symmetry-Protected Topological Triangular Weyl Complex
• Phononic Helical Nodal Lines with $\mathcal{P}\mathcal{T}$ Protection in MoB${}_2$
• Topological Thermoelectricity in Metals
• Diagnosis for topological semimetals in the absence of spin-orbital coupling
• Topological spin excitations observed in a three-dimensional antiferromagnet
• Twofold quadruple Weyl nodes in chiral cubic crystals
• Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Symmetry-Enforced Weyl Phonons
• Discovery of coexisting Dirac and triply degenerate magnons in a three-dimensional antiferromagnet
• Topological circuits of inductors and capacitors
• Phononic Weyl Nodal Straight Lines in High-Temperature Superconductor MgB${}_2$
• Intrinsically polar elastic metamaterials
• Experimental Realization of a Reconfigurable Electroacoustic Topological Insulator
• Topological phonons in oxide perovskites controlled by light
• Soft self-assembly of Weyl materials for light and sound
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• Straight nodal-line phonons in symmorphic space groups
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Charge-4 Weyl point: Minimum lattice model and chirality-dependent properties
• Weyl phonons in chiral crystals
• Symmetry-enforced ideal lantern-like phonons in ternary nitride Li${}_6$WN${}_4$
• Topology in non-linear mechanical systems
• Coexistience of phononic six-fold, four-fold and three-fold excitations in ternary antimonide Zr3Ni3Sb4
• Magnonic Analogs of Topological Dirac Semimetals
• Directional mechanical response in the bulk of topological metamaterials
• Chiral phonons in honeycomb sublattice of layered CoSn-like compounds
• Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP
• Universal Continuum Theory for Topological Edge Soft Modes
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Signatures of Weyl fermion annihilation in a correlated kagome magnet
• Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide
• Topology of Triple-Point Metals
• What's knot to like? Observation of a linked loop quantum state
• Topological thermal Hall effect driven by fluctuation of spin chirality in frustrated antiferromagnets
• Soft mechanical metamaterials with transformable topology protected by stress caching
• Calculated magnetic exchange interactions in Dirac magnon material Cu3TeO6
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Signatures of Topological Phonons in Superisostatic Lattices
• Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
• Fragile phonon topology on the honeycomb lattice with time-reversal symmetry
• Topological Node-Lines in Mechanical Metacrystals
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Topological Flexural Modes in Polarized Bilayer Lattices
• Anharmonic theory of superconductivity and its applications to emerging quantum materials
• Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Topological band structure of surface acoustic waves on a periodically corrugated surface
• Orbital-Active Dirac Materials from the Symmetry Principle
• Topological mechanical metamaterial with nonrectilinear constraints
• Topological phonons in arrays of ultracold dipolar particles
• Scalable 3D printing for topological mechanical metamaterials
• Chiral Topological Phononic Quasiparticles in Enantiomeric Crystals SrSi${}_2$ and BaSi${}_2$
• Concurrence of topological electrons and magnons in the Kagome ferromagnet CoCu3(OH)6Cl2
• Classifying topological floppy modes in the continuum
• Cell augmentation framework for topological lattices
• Signatures of a topological Weyl loop in Co${}_3$Sn${}_2$S${}_2$
• Phonon Weyl points and chiral edge modes with unconventional Fermi arcs in NbSi${}_2$
• 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies
• The mechanical modes of a $2$-periodic triangulated surface
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Topological Weyl-like Phonons and Nodal Line Phonons in Graphene