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.

arXiv comment22 + 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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• 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
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• Quantum Valley Hall effect without Berry curvature
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
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• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Observation of squeezed Chern insulator in an acoustic fractal lattice
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• Real Hopf Insulator
• Photonic nodal lines with quadrupole Berry curvature distribution
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• 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
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