Square-root topological state of coupled plasmonic nanoparticles in a decorated Su–Schrieffer–Heeger lattice

Wu, Huaming; Wei, Guochao; Liu, Zhen Zhen; Xiao, Jun Jun

doi:10.1364/ol.434306

Cited by 20 publications

(6 citation statements)

References 24 publications

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“…As the spacing of the particles is large enough compared to the radius (2c, d − 2c ≥ 3a), the i-th nanospheres can be treated as dipoles with dipole moments p i located at r i [21]. Therefore, the system is described by the coupled dipole equations [15,18,19,[22][23][24][25][26][27] 1 α(ω)…”

Section: Coupled Dipole Model -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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Section: Coupled Dipole Model -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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“…Inheriting the topological properties from the parent Hamiltonian, non-zero energy corner states at non-central bandgaps of the symmetry spectra arise after the square-root operation. Strikingly, the squareroot higher-order topological insulators have been observed in sonic crystals [34][35][36], photonic crystals [37,38], electric circuits [39,40]. Moreover, the notion of square root topology is applied to study topological skin effect in non-Hermitian 1D photonic crystals [41].…”

Section: Introductionmentioning

confidence: 99%

Third-order square-root topological insulators on decorated diamond sonic crystals

Geng

Shen

Duan

et al. 2023

J. Phys.: Condens. Matter

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The square-root operation can generate novel topological phases, whose nontrivial topological properties are inherited from the parent Hamiltonian. Here we report the acoustic realization of third-order square-root topological insulators by adding additional resonators between the site resonators of original diamond lattice. Due to the square-root operation, multiple acoustic localized modes appear in doubled bulk gaps. The bulk polarizations of the tight-binding models are employed to reveal the topological feature of the higher-order topological states. By tuning the coupling strength, we find the emergence of third-order topological corner states in doubled bulk gaps on tetrahedron-like and rhombohedron-like sonic crystals, respectively. The shape dependence of square-root corner states provides an extra degree of freedom for flexible manipulation on the sound localization. Furthermore, the robustness of the corner states in 3D square-root topological insulator is well elucidated by introducing random disorders into the irrelevant bulk region of the proposed 3D lattices. This work extends square-root higher-order topological states into three-dimensional (3D) system, and may find possible applications in selective acoustic sensors.

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“…In the context of topological materials, there has been a resurgence of Dirac's original intuition with the advent of square-root topological insulators and also square-root Weyl semi-metals. Both systems emerge by taking the square root of either an appropriate tight-binding model [3] which can lead to a new class of topological insulator that allows robust edge states with codimension larger than one [4][5][6][7][8][9][10][11] or by stacking such two-dimensional (2D) squareroot higher-order topological insulators with interlayer couplings in a double-helix pattern [12]. While both might seem artificial, the former has been observed in a photonic cage [13].…”

Section: Introductionmentioning

confidence: 99%

Kitaev Chain with a Fractional Twist

Basa,

La Nave,

Phillips

2022

Preprint

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The topological non-triviality of insulating phases of matter are by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in Q. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[1] demonstrating that projective Dirac operators defined in the absence of spin C structure have rational indices.

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Square-root topological state of coupled plasmonic nanoparticles in a decorated Su–Schrieffer–Heeger lattice

Cited by 20 publications

References 24 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

Third-order square-root topological insulators on decorated diamond sonic crystals

Kitaev Chain with a Fractional Twist

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Square-root topological state of coupled plasmonic nanoparticles in a decorated Su–Schrieffer–Heeger lattice

Cited by 20 publications

References 24 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

Third-order square-root topological insulators on decorated diamond sonic crystals

Kitaev Chain with a Fractional Twist

Contact Info

Product

Resources

About

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