Nodal rings and drumhead surface states in phononic crystals

Deng, Weiyin; Lu, Jiuyang; Li, Feng; Huang, Xueqin; Yan, Mou; Ma, Jiahong; Liu, Zhengyou

doi:10.1038/s41467-019-09820-8

Cited by 95 publications

(60 citation statements)

References 33 publications

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“…Instead of the Hamiltonian, it is the Laplacian J that determines the steady state behavior of a circuit via I = JV, where I and V are the input currents and potentials at all the nodes. Since the circuit engineering of desired Laplacian is a mature topic [48,49,68,69] with Hermitian nodal drumhead states even experimentally measured [46,70,71], we shall relegate its details to the Supplement [55]. As illustrated in Fig.…”

Section: Discussionmentioning

confidence: 99%

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Lee

Li²,

Liu

et al. 2020

Preprint

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The paradigm of metals has undergone a revision and diversification from the viewpoint of topology. Non-Hermitian nodal knot metals (NKMs) constitute a class of matter without Hermitian analog, where the intricate structure of complex-valued energy bands gives rise to knotted lines of exceptional points and new topological surface state phenomena. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their underlying parent knots, and complement our results by an optimized constructive ansatz that provides tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. In particular, we identify the surface state boundaries as ``tidal' intersections of the complex band structure in a marine landscape analogy. We further find these tidal surface states to be intimately connected to the band vorticity and the layer structure of their dual Seifert surface, and as such provide a fingerprint for non-Hermitian NKMs.

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Section: Discussionmentioning

confidence: 99%

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Lee

Li²,

Liu

et al. 2020

Preprint

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“…As it turns out, Weyl points are only one member of a broader family of topologically nontrivial band degeneracies. Researchers have demonstrated photonic/acoustic crystals with topological nodal lines—band degeneracies lying along one-dimensional (1D) curves in momentum space—which are associated with Berry phase winding of π and drumhead surface states 23–26 . Recent theoretical studies have also revealed the possibility of higher-dimensional topological band degeneracies, such as twofold two-dimensional (2D) nodal surfaces 27–34 .…”

Section: Introductionmentioning

confidence: 99%

Observation of a topological nodal surface and its surface-state arcs in an artificial acoustic crystal

et al. 2019

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Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces. Both nodal points and nodal lines have been realized recently in photonics and acoustics. However, a nodal surface has never been observed in any classical-wave system. Here, we report on the experimental observation of a twofold symmetry-enforced nodal surface in a 3D chiral acoustic crystal. In particular, the demonstrated nodal surface carries a topological charge of 2, constituting the first realization of a higher-dimensional topologically-charged band degeneracy. Using direct acoustic field measurements, we observe the projected nodal surface and its Fermi-arc-like surface states and demonstrate topologically-induced robustness of the surface states against disorders. This discovery of a higher-dimensional topologically-charged band degeneracy paves the way toward further explorations of the physics and applications of new topological semimetal phases.

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“…Note that a very recent work by S. Zhang et al has made the first step toward the experimental study of 3D Dirac points in classical wave systems28 .Interestingly, the Dirac points are constructed by electromagnetic duality symmetry (which are unique in electromagnetic systems), also strikingly different from the crystalline symmetry involved here. Starting with our structure, one can design 10 various interesting 3D acoustic topological states (e.g., Weyl points29,31 and line nodes37,38 ) through symmetry reduction. Here we would like to mention that, more or less, there is dissipation loss in our airborne phononic crystal, which may introduce a non-Hermitian modification in the effective Hamiltonian.…”

mentioning

confidence: 99%

Symmetry-enforced three-dimensional Dirac phononic crystals

Cai

Qiu

et al. 2020

Light Sci Appl

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Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases.Such gapless topological states have been accomplished by a band-inversion mechanism, in which the Dirac points can be annihilated pairwise by perturbations without changing the symmetry of the system. Here, we report an experimental observation of Dirac points that are enforced completely by the crystal symmetry, using a nonsymmorphic three-dimensional phononic crystal. Intriguingly, our Dirac phononic crystal hosts four spiral topological surface states, in which the surface states of opposite helicities intersect gaplessly along certain momentum lines, as confirmed by our further surface measurements. The novel Dirac system may release new opportunities for studying the elusive (pseudo)relativistic physics, and also offer a unique prototype platform for acoustic applications.

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Nodal rings and drumhead surface states in phononic crystals

Cited by 95 publications

References 33 publications

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Tidal surface states as ﬁngerprints of non-Hermitian nodal knot metals

Observation of a topological nodal surface and its surface-state arcs in an artificial acoustic crystal

Symmetry-enforced three-dimensional Dirac phononic crystals

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