Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is ch
aracterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless helical edge states, and zero-dimensional corner states coexist in the same system. The new hybrid-order topological phase may produce novel applications in topological acoustic devices.
The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored first-order topologi
cal insulators described by the Z_2 index. However, most recently, a proposal asserts that a significant bridge can be established between the HOTIs and the Z_2 topological insulators. When subject to an in-plane Zeeman field, the corner states, the signature of the HOTIs, can be induced in a Z_2 topological insulator. Such Zeeman field can be produced, for example, by the ferromagnetic proximity effect or magnetic atom doping, which obviously involves the drastically experimental complexity. Here we show that, a phononic crystal, designed as a bilayer of coupled acoustic cavities, hosts exactly the Kane-Mele model with built-in in-plane Zeeman fields. We observe that the helical edge states along the zigzag edges are gapped, and the corner states, localized spatially at the corners of the samples, appear in the gap, confirming the effect induced by the Zeeman field. We further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.
Topological semimetal, hosting spin-1 Weyl point beyond Dirac and Weyl points, has attracted a great deal of attention. However, the spin-1 Weyl semimetal, which possesses exclusively the spin-1 Weyl points in a clean frequency window, without shadow
ed by any other nodal points, is yet to be discovered. Here, we report for the first time a spin-1 Weyl semimetal in a phononic crystal. Its spin-1 Weyl points, touched by two linear dispersions and an additional flat band, carry monopole charges (-2,0,2) or (2,0,-2) for the three bands from bottom to top, and result in double Fermi arcs existing both between the 1st and 2nd bands, as well as between the 2nd and 3rd bands. We further observe robust propagation against the multiple joints and topological negative refraction of acoustic surface arc wave. Our results pave the way to explore on the macroscopic scale the exotic properties of the spin-1 Weyl physics.
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered on that p
romise in the electronic realm through high-precision metrology devices. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we use a two-dimensional acoustic crystal with two layers to mimic spin-orbit coupling, a crucial ingredient of topological insulators. In particular, our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing spin Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. Moreover, in an H-shaped device we demonstrate how the transport path can be selected by tuning the geometry, enabling the construction of complex networks.
Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could promote the deep development and utilization of the Weyl physics. Although the ideal type-I Weyl points have been achieved in photonic crystals, the ideal t
ype-II Weyl points with tilted cone-like band dispersions, are still beyond discovery. Here we realize ideal type-II Weyl points of minimal number in three-dimensional layer-stacked phononic crystals, and demonstrate topological phase transition from Weyl semimetal to valley insulators of two distinct types. The Fermi-arc surface states exist on the interface of the Weyl and valley phases, while the Fermi-circle ones occur on that of the two distinct valley phases. We show the interesting wave partition of Fermi-circle surface states on the interfaces formed by distinct valley phases.
Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of t
riangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices, can be anticipated by the intriguing acoustic edge states enriched by the layer information.
The artificial crystals for classical waves provide a good platform to explore the topological physics proposed originally in condensed matter systems. In this paper, acoustic Dirac degeneracy is realized by simply rotating the scatterers in sonic cr
ystals, where the degeneracy is induced accidentally by modulating the scattering strength among the scatterers during the rotation process. This gives a flexible way to create topological phase transition in acoustic systems. Edge states are further observed along the interface separating two topologically distinct gapped sonic crystals.
Valley pseudospin, labeling quantum states of energy extrema in momentum space, is attracting tremendous attention1-13 because of its potential in constructing new carrier of information. Compared with the non-topological bulk valley transport realiz
ed soon after predictions1-5, the topological valley transport in domain walls6-13 is extremely challenging owing to the inter-valley scattering inevitably induced by atomic scale imperfectness, until the recent electronic signature observed in bilayer graphene12,13. Here we report the first experimental observation of topological valley transport of sound in sonic crystals. The macroscopic nature of sonic crystals permits the flexible and accurate design of domain walls. In addition to a direct visualization of the valley-selective edge modes through spatial scanning of sound field, reflection immunity is observed in sharply curved interfaces. The topologically protected interface transport of sound, strikingly different from that in traditional sound waveguides14,15, may serve as the basis of designing devices with unconventional functions.
