Boundary Criticality of 
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-Invariant Topology and Second-Order Nodal-Line Semimetals

Wang, Kai; Dai, Jia-Xiao; Shao, L. B.; Yang, Shengyuan A.; Zhao, Y. X.

doi:10.1103/physrevlett.125.126403

Cited by 80 publications

(50 citation statements)

References 42 publications

(47 reference statements)

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“…Interest is growing in the study of multi-gap topologies [22][23][24][25][26][27] , with recent developments including new dynamical quench signatures 28 and a very recent realisation in an acoustic metamaterial 15 . Despite these advances, the multi-gap condition is complicated by the Fermi-Dirac distribution of electrons in materials, and as a result multi-gap topology has not yet been observed in real materials.…”

mentioning

confidence: 99%

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

et al. 2022

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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 Γ 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.

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confidence: 99%

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

et al. 2022

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“…We show that the real Chern number of a generalized Dirac point in PT -symmetric Dirac semimetals [69,70] can be extracted from the quantum-metric measurement. The Bloch Hamiltonian in three-dimensional momentum space of the real Dirac semimetals is given by…”

Section: A Extracting the Real Chern Numbermentioning

confidence: 98%

Extracting non-Abelian quantum metric tensor and its related Chern numbers

Ding,

Zhu,

et al. 2022

Preprint

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The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.

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“…Such a phase belongs to the category of so called fragile topology that can be trivialized by adding trivial bands [16], in stark contrast to a stable topology which remains nontrivial upon adding trivial bands. In this context, a class of topological phases protected by space-time inversion symmetry is highlighted [20,[22][23][24][25][26][27][28][29]. Among them, the Euler class characterizing the topological property of twodimensional real wave functions underlies the failure of the Nielsen-Ninomiya theorem [20] and the existence of Wilson loop winding [22].…”

Section: Introductionmentioning

confidence: 99%

Observation of topological Euler insulators with a trapped-ion quantum simulator

Zhao¹,

Yang²,

Jiang³

et al. 2022

Preprint

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Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the twodimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments.

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Boundary Criticality of PT -Invariant Topology and Second-Order Nodal-Line Semimetals

Cited by 80 publications

References 42 publications

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

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

Extracting non-Abelian quantum metric tensor and its related Chern numbers

Observation of topological Euler insulators with a trapped-ion quantum simulator

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