Acoustic higher-order topological insulator on a kagome lattice

Xue, Haoran; Yang, Yahui; Gao, Fei; Chong, Yidong; Zhang, Baile

doi:10.1038/s41563-018-0251-x

Cited by 807 publications

(497 citation statements)

References 31 publications

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“…Furthermore, the artifact effect of the corner states are also discussed in Supplementary Note 4. These findings echo the observations in photonic and phononic systems [13][14][15][16][17][18][19][20][21].…”

Section: Corner States and Phase Diagramsupporting

confidence: 88%

“…However, a higher-order, e.g., kth-order, topological insulator allows (n − k)-dimensional topological boundary states with 2 k n, which goes beyond the standard bulk-boundary correspondence and is characterized by the bulk topological index [5][6][7][8][9][10][11][12]. Interestingly, the experimental evidences of higher-order topological insulators (HO-TIs) were reported so far only in classical mechanical and electromagnetic metamaterials [13][14][15][16][17][18][19][20][21]. In terms of applications of HOTIs in spintronics, it is intriguing to ask if they can exist in magnetic system which is intrinsically, however nonlinear, in contrast to its phononic and photonic counterparts.…”

Section: Introductionmentioning

confidence: 99%

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Higher-order topological solitonic insulators

Cao

Peng

et al. 2019

npj Comput Mater

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Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we theoretically study the dipolar-coupled gyration motion of magnetic solitons on the twodimensional breathing kagome lattice. We calculate the phase diagram and predict both the Tamm-Shockley edge modes and the second-order corner states when the ratio between alternate lattice constants is greater than a critical value. We show that the emerging corner states are topologically robust against both structure defects and moderate disorders. Micromagnetic simulations are implemented to verify the theoretical predictions with an excellent agreement. Our results pave the way for investigating higher-order topological insulators based on magnetic solitons. arXiv:1909.11511v1 [cond-mat.mes-hall]

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Section: Corner States and Phase Diagramsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Higher-order topological solitonic insulators

Cao

Peng

et al. 2019

npj Comput Mater

View full text Add to dashboard Cite

show abstract

“…In addition, Eq. (12) implies that the virtual legs on the A and B sublattices transform as hole-like and particle-like degrees of freedom (DOFs), respectively.…”

Section: Local Tensors and U(1) Symmetrymentioning

confidence: 99%

Fermionic tensor networks for higher-order topological insulators from charge pumping

et al. 2020

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We apply the charge pumping argument to fermionic tensor network representations of ddimensional topological insulators (TIs) to obtain tensor network states (TNSs) for (d + 1)dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair state (PEPS) for a Chern insulator starting from a matrix product state (MPS) in d = 1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to secondorder TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d = 2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d + 1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest neighbour Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively. arXiv:1912.08219v1 [cond-mat.str-el]

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“…The usual route to study these phenomena in continuous classical systems is to achieve particular designs which are analogs of discrete models with topological characteristics [17,18]. That way, it is expected that the proposed continuous wave systems will inherit the topological properties of these discrete models, especially regarding the robust transfer of protected states [19][20][21]. One of the first and most thoroughly studied models in the field of condensed matter is the honeycomb discrete tight-binding model, which was originally used to describe the electronic properties of graphene.…”

Section: Introductionmentioning

confidence: 99%

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

et al. 2020

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In this work, we study the propagation of sound waves in a honeycomb waveguide network loaded with Helmholtz resonators (HRs). By using a plane wave approximation in each waveguide we obtain a first-principle modeling of the network, which is an exact mapping to the graphene tight-binding Hamiltonian. We show that additional Dirac points appear in the band diagram when HRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edge modes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interface modes located in the band gap, and these modes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedom bestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also of more complex systems.

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Acoustic higher-order topological insulator on a kagome lattice

Cited by 807 publications

References 31 publications

Higher-order topological solitonic insulators

Higher-order topological solitonic insulators

Fermionic tensor networks for higher-order topological insulators from charge pumping

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

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