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

Abstract

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 $\Gamma$ 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.

26 pages, 8 figures

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• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Quantized Integrated Shift Effect in Multigap Topological Phases
• Optical manifestations and bounds of topological Euler class
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Topological continuum charges of acoustic phonons in 2D
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Non-Abelian Hopf-Euler insulators
• Landau Levels of the Euler Class Topology
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Quantum Valley Hall effect without Berry curvature
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Interferometry of non-Abelian band singularities and Euler class topology
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Projected spin texture as a bulk indicator of fragile topology
• Hermitian Topologies originating from non-Hermitian braidings
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Monolayer C${}_{60}$ networks: A first-principles perspective
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Hybrid nodal surface and nodal line phonons in solids
• Anomalous geometric transport signatures of topological Euler class
• Exact projected entangled pair ground states with topological Euler invariant
• Andreev reflection in Euler materials
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Optical signatures of Euler superconductors
• Second Euler number in four dimensional synthetic matter
• Floquet non-Abelian topological charges and edge states
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Omnidirectional domain wall modes protected by fragile topological states
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
• Euler band topology in superfluids and superconductors
• Non-Abelian interference of topological edge states
• Coupled-wire construction of non-Abelian higher-order topological phases
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Three-dimensional spinless Euler insulators with rotational symmetry
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Emergence of Nodal-Knot Transitions by Disorder