Elastic Higher-Order Topological Insulator with Topologically Protected Corner States

Fan, Haiyan; Xia, Baizhan; Tong, Liang; Zheng, Shengjie; Yu, Dejie

doi:10.1103/physrevlett.122.204301

Cited by 284 publications

(117 citation statements)

References 58 publications

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“…Higher-order topological insulators have recently drawn research interest as new topological crystalline phases 1- 30 . Unlike conventional first-order topological insulators, two-dimensional (2D) second-order topological insulators (SOTIs) have topologically protected corner states, and three-dimensional (3D) SOTIs have topological gapless modes on the hinges.…”

Section: Introductionmentioning

confidence: 99%

Second-order topological phases protected by chiral symmetry

Okugawa

Hayashi

Nakanishi³

2019

Phys. Rev. B

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We study second-order topological phases characterized by chiral symmetry in the absence of crystal symmetries. We investigate topological phase transitions of a model for the two-dimensional second-order topological insulators protected by chiral symmetry. By the theory of the phase transitions, we propose chiral-symmetric second-order topological semimetals. Various second-order topological semimetals can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry allows a topological phase transition from the second-order topological semimetal to a second-order topological insulator with chiral hinge states in the three-dimensional system. We also demonstrate the secondorder topological phases by using a lattice model.

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Section: Introductionmentioning

confidence: 99%

Second-order topological phases protected by chiral symmetry

Okugawa

Hayashi

Nakanishi³

2019

Phys. Rev. B

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“…Moreover, the connection between corner and hinge states and bulk defects can also be generalized to any model with a vectorial mass generating the bulk gap. This covers, for example, systems with reflection and/or discrete rotational symmetries [33,44]. As the frequency is lowered in these protocols, we would expect a series of transitions with multiple bulk Floquet bound states appearing at the Floquet zone edge and center.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…For example, a two-dimensional electric quadrupole topological insulator binds corner states with fractional charge e/2. Such higher-order topological phases have been predicted to exist in engineered lattices of cold atoms [23] and in natural elemental bismuth [27], and have been observed in a mechanical system of coupled microwave resonators [28,29], optical waveguides [30], topolectrical circuits [31], mechanical metamaterials [32], and elastic acoustic structures [33]. In this work, we show that higher-order Floquet topological phases can be realized and controlled in a periodically driven system, supporting lower-dimensional Floquet bound states at the Floquet zone center and/or edge.…”

Section: Introductionmentioning

confidence: 96%

Higher-order Floquet topological phases with corner and bulk bound states

2019

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We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order "anomalous" Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This "stirring drive protocol" leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification and offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states. arXiv:1811.04808v2 [cond-mat.mes-hall]

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“…To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems.…”

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confidence: 99%

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

et al. 2019

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in 2D system. To date, HOTIs have been theoretically predicted and experimentally realized in elastics, [34,35] microwaves, [36] electric circuits, [37] photonics, [38][39][40] and acoustic systems. [41][42][43][44][45][46] In order to make HOTIs more attractive for real-world applications as in sound wave control, several hurdles must be overcome. For example, most of the reported results focus solely on a single frequency band, whose limitations ought to be overcome in order to provide a broadband response for topologically robust acoustics. Also, the above reported acoustic implementations have, for the most part, been implemented inside waveguides or were designed in an acoustically rigid enclosure, which hinders their capabilities from external insonification. Lastly, in terms of compactness, it is desired to utilize building blocks of the HOTI on a subwavelength scale in order to confine sound in tight areas beyond the diffraction limit.In this work, we design topologically protected acoustic corner states at deep subwavelength scales by constructing a perforated crystal, also known as holey metamaterials. The advantage in using holey metamaterials resides in their high levels of integration and miniaturization at scales much smaller than the sound wavelength. Without being pierced by holes, those metamaterials would not be able to sustain surface-confined wave propagation. With perforations on the other hand, externally incident radiation is able to bind to the structure in the form of "spoof" surface acoustic waves (SAWs), thus enabling sound energy confinement way beyond the classical diffraction limit. [47,48] In addition to breaking the diffraction limit for spoof SAWs, we demonstrate that a topological phase transition, which is derived from an extended 2D Zak phase, can be tuned by simply shrinking or expanding the distance among a group of holes within the unit cell. Beyond measuring corner states within multiple nontrivial bandgaps, the first-order resonance in particular displays the strongest topological sound energy confinement down to a feature size of λ/50. Lastly, we experimentally verify their resilience against defects and design a HOTI device for topological subwavelength imaging, which may be relevant for sound energy focusing and detection. Figure 1a illustrates the schematic of deep-subwavelength acoustic SOTI under consideration, which is realized by a perforated rigid material whose holes are arranged in a square lattice. The perforation depth and the radii of holes are H = 12 cm and r = 0.5 cm, respectively. The lattice constant is a = 4.8 cm.The center-to-center distance between the adjacent holes in the unit cell is defined as R, which is chosen to be R/a = 0.5 for the Higher-order topological insulators (HOTIs) belong to a new class of materials with unusual topological phases. They have garnered considerable attention due to their capabilities in confining energy at the hinges and corners, which is entirely protected by the topology, and have thus become attractive structures for...

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Elastic Higher-Order Topological Insulator with Topologically Protected Corner States

Cited by 284 publications

References 58 publications

Second-order topological phases protected by chiral symmetry

Second-order topological phases protected by chiral symmetry

Higher-order Floquet topological phases with corner and bulk bound states

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

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