Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays

Kang, Juan; Liu, Tao; Yan, Mou; Yang, Dandan; Huang, Xiongjian; Wei, Ruishan; Qiu, Jianrong; Dong, Guoping; Yang, Zhongmin; Nori, Franco

doi:10.48550/arxiv.2109.00879

Cited by 3 publications

(1 citation statement)

References 46 publications

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“…For the 2D case, a second-order topological insulator hosts 1D gapped edge states and 0D CSs. So far, HOTIs have been theoretically and experimentally investigated in microwave [4], circuit [5], waveguide arrays [6,7], photonic and sonic crystals [8,9].…”

mentioning

confidence: 99%

Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays

Luo,

Li,

Shen

et al. 2023

EPL

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A profound insight into topological photonic systems will empower us to harness their maximum potential and discover uncharted topological phenomena. For the square quadripartite lattice with only nearest-neighbor reciprocal couplings, in the out-of-plane mode, sublattice symmetry makes the eigenvalues of Hamiltonian symmetric around zero energy, while C4 symmetry closes the gap between the central bands. Meanwhile, topological corner states (CSs) are fixed at zero energy due to chiral symmetry. Thereby, the CSs cannot appear in a gap, but are embedded in the bulk. In this paper, the full coupling between dipoles is considered in the Hamiltonian, i.e., not only the near-field of nearest-neighbor, but also far-field dipole-dipole interactions are taken into account to investigate the new potential topological properties. The results show that sublattice symmetry of the system will be broken, leading to appearance of zero-energy band gap. Nevertheless, the generalized chiral symmetry ensures that the CSs are still pinned to zero energy. That is, in-gap CSs are provided. Additionally, the silicon carbide materials used in this paper can confine light to the deep subwavelength scale, which has great potential in enhancing light-matter interactions in the terahertz rang.

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mentioning

confidence: 99%

Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays

Luo,

Li,

Shen

et al. 2023

EPL

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Square-root higher-order Weyl semimetals

et al. 2022

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The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances, such as the prediction of positron, a direct outcome of the Dirac equation which stems from the square-root of the Klein-Gordon equation. In this article, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both “Fermi-arc” surface and hinge states that respectively connect the projection of the Weyl points on the side surface and arris. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.

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Realization of second-order photonic square-root topological insulators

Yan¹,

Song²,

Xia³

et al. 2021

Preprint

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Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays

Cited by 3 publications

References 46 publications

Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays

Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays

Square-root higher-order Weyl semimetals

Realization of second-order photonic square-root topological insulators

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Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays

Cited by 3 publications

References 46 publications

Topological robust corner states of a two-dimensional square lattice with C4 symmetry in fully coupled dipolar arrays

Topological robust corner states of a two-dimensional square lattice with C4 symmetry in fully coupled dipolar arrays

Square-root higher-order Weyl semimetals

Realization of second-order photonic square-root topological insulators

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Product

Resources

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Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays

Topological robust corner states of a two-dimensional square lattice with C₄ symmetry in fully coupled dipolar arrays