Square-root higher-order Weyl semimetals

Song, Lizhu; Yang, Huanhuan; Cao, Yunshan; Peng, Yan

doi:10.1038/s41467-022-33306-9

Cited by 35 publications

(9 citation statements)

References 52 publications

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“…Different from topological insulators, TSMs are typically gapless since they host band touching/crossing in the bulk bands, as encountered with 3D Dirac or Weyl points. In particular, higher-order topological semimetal (HOTSM) phases in 3D structures have been predicted and experimentally realized in acoustic, electric circuits and photonic systems, featuring for example, 1D hinge states. − However, previous experimental studies of HOTSMs have mostly been carried out using 3D platforms, focusing on exploring the HOTSM phases in 3D gapless systems. To the best of our knowledge, zero-dimensional corner states have thus far not been realized in any 2D TSM-like gapless systems.…”

Section: Introductionmentioning

confidence: 99%

Realization of Topological Corner States in Tailored Photonic Graphene

Xie,

Yan,

Xia

et al. 2024

ACS Photonics

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Higher-order topological semimetals (HOTSMs) represent a novel type of gapless topological phase, hosting boundary states with dimensions at least two lower than those of their bulk geometry. Such nontrivial boundary states have been predicted and observed in three-dimensional (3D) gapless topological systems, representing features of the HOTSMs. However, their two-dimensional (2D) analogs, represented especially by the corner states in monolayer graphene-like structures, have thus far remained only a theoretical exploration. Here, we experimentally demonstrate nontrivial corner states in specially tailored photonic graphene hosting Dirac points, manifesting the HOTSM-like property in a 2D photonic setting. Such corner states in the otherwise gapless system exhibit distinct phase structures depending on the lattice corner and edge geometry, and are completely degenerate with the zero-energy edge states. Remarkably, we find that these "gapless" corner states remain intact at zero-energy even in a finite-sized graphene lattice, protected by chiral symmetry. Unlike corner states in higher-order topological insulators or topological crystalline insulators with certain rotational symmetry, these corner states are localized exclusively to one corner without any coupling to the bulk or other corners, despite longdistance propagation.

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Section: Introductionmentioning

confidence: 99%

Realization of Topological Corner States in Tailored Photonic Graphene

Xie,

Yan,

Xia

et al. 2024

ACS Photonics

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“…Recently, a square-root TI (SRTI) is proposed 32 . Its topological properties are demonstrated to be inherited from the parent Hamiltonian [33][34][35][36] . The square-root procedure had played an important role in deriving the Dirac equation in relativistic quantum mechanics from the quadratic Klein-Gordon equation, which revealed the chirality for electrons.…”

Section: Introductionmentioning

confidence: 99%

Observation of Multiple Topological edge States in Square-Root electric circuits

Gao,

Zhang,

Cheng

et al. 2024

AJST

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Square-root topological states are new topological phases, whose intriguing topological properties are inherited from the parent lattice Hamiltonian. Because of the square-root procedure, the bulk gap of the parent Hamiltonian is doubled. In this letter, we report the observation of the square-root topological insulators (SRTIs) in topological LC circuits, whose squared Hamiltonian includes a Su-Schrieffer-Heeger (SSH) model, a well-known example of topological insulators (TI). The multiple localized edge states falling in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. These edge states with zero energy are manifested by a prominent impedance peak at the midgap frequency and directly observed by impedance measurements. Our work opens up an alternative gateway towards actively controllable topological systems and may bring about new possibilities in topology-driven electronic devices.

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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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Square-root higher-order Weyl semimetals

Cited by 35 publications

References 52 publications

Realization of Topological Corner States in Tailored Photonic Graphene

Realization of Topological Corner States in Tailored Photonic Graphene

Observation of Multiple Topological edge States in Square-Root electric circuits

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

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