Observation of non-Abelian topological semimetals and their phase transitions

Abstract

Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have almost exclusively been restricted to single-gap band topology because of the Fermi-Dirac filling effect. Here, we theoretically analyze and experimentally confirm a novel class of multi-gap topological phases, which we will refer to as non-Abelian topological semimetals, on kagome geometries. These unprecedented forms of matter depend on the notion of Euler class and frame charges which arise due to non-Abelian charge conversion processes when band nodes of different gaps are braided along each other in momentum space. We identify such exotic phenomena in acoustic metamaterials and uncover a rich topological phase diagram induced by the creation, braiding and recombination of band nodes. Using pump-probe measurements, we verify the non-Abelian charge conversion processes where topological charges of nodes are transferred from one gap to another. Moreover, in such processes, we discover symmetry-enforced intermediate phases featuring triply-degenerate band nodes with unique dispersions that are directly linked to the multi-gap topological invariants. Furthermore, we confirm that edge states can faithfully characterize the multi-gap topological phase diagram. Our study unveils a new regime of topological phases where multi-gap topology and non-Abelian charges of band nodes play a crucial role in understanding semimetals with inter-connected multiple bands.

22 + 19 pages, 5+11 figures. With regard to references, please note that this concerns a version submitted to the journal in February 2021

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• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Topological thermal transport
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• Minimal non-abelian nodal braiding in ideal metamaterials
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
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• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
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• 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
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Non-Abelian Braiding of Topological Edge Bands
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
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• Tilted Dirac cones and topological transitions in strained kagome lattices
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
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• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Machine Learning of Knot Topology in Non-Hermitian Band Braids
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• Photonic nodal lines with quadrupole Berry curvature distribution
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
• Hermitian Topologies originating from non-Hermitian braidings
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Projected spin texture as a bulk indicator of fragile topology
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Anomalous geometric transport signatures of topological Euler class
• Statistical learning of engineered topological phases in the kagome superlattice of AV${}_3$Sb${}_5$
• Hybrid nodal surface and nodal line phonons in solids
• Andreev reflection in Euler materials
• Exact projected entangled pair ground states with topological Euler invariant
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Unpaired topological triply degenerate point for spin-tensor-momentum-coupled ultracold atoms
• Topological Corner Modes by Composite Wannier States in Glide-Symmetric Photonic Crystal
• Observing the nodal-line conversion determined by the relative homotopy
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Optical signatures of Euler superconductors
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• Encyclopedia of emergent particles in three-dimensional crystals
• Second Euler number in four dimensional synthetic matter
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Polarization textures in crystal supercells with topological bands
• Differences between quantum and classical adiabatic evolution
• Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
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• Anomalous multi-gap topological phases in periodically driven quantum rotors
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• Floquet composite Dirac semimetals
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• Orbital magnetization reveals multiband topology
• Hinge modes of three-dimensional Euler insulators
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc
• Three-dimensional spinless Euler insulators with rotational symmetry
• Emergence of Nodal-Knot Transitions by Disorder
• Coupled-wire construction of non-Abelian higher-order topological phases