Probing Weyl Physics with One-Dimensional Sonic Crystals

Bound-Extended Mode Transition in Type-II Synthetic Photonic Weyl Heterostructures

Photonic structures with Weyl points (WPs), including type I and type II, promise nontrivial surface modes and intriguing light manipulations for their three-dimensional topological bands. While previous studies mainly focus on exploring WPs in a uniform Weyl structure, here we establish Weyl heterostructures (i.e., a nonuniform Weyl lattice) with different rotational orientations in the synthetic dimension by nanostructured photonic waveguides. In this work, we unveil a transition between bound and extended modes on the interface of type-II Weyl heterostructures by tuning their rotational phases, despite the reversed topological order across the interface. This mode transition is also manifested from the total transmission to total reflection at the interface. All of these unconventional effects are attributed to the tilted dispersion of type-II Weyl band structure that can lead to mismatched bands and gaps across the interface. As a comparison, the type-I Weyl heterostructures lack the phase transition due to the untilted band structure. This work establishes a flexible scheme of artificial Weyl heterostructures that opens a new avenue toward high-dimensional topological effects and significantly enhances our capabilities in on-chip light manipulations.

Fermi Arc Reconstruction in Synthetic Photonic Lattice

The chiral surface states of Weyl semimetals have an open Fermi surface called a Fermi arc. At the interface between two Weyl semimetals, these Fermi arcs are predicted to hybridize and alter their connectivity. In this Letter, we numerically study a one-dimensional (1D) dielectric trilayer grating where the relative displacements between adjacent layers play the role of two synthetic momenta. The lattice emulates 3D crystals without time-reversal symmetry, including Weyl semimetal, nodal line semimetal, and Chern insulator. Besides showing the phase transition between Weyl semimetal and Chern insulator at telecom wavelength, this system allows us to observe the Fermi arc reconstruction between two Weyl semimetals, confirming the theoretical predictions.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Observation of Weyl Interface States in Non-Hermitian Synthetic Photonic Systems

Weyl medium has triggered remarkable interest owing to its nontrivial topological edge states in 3D photonic band structures that were mainly revealed as surface modes yet. It is undoubted that the connection of two different Weyl media will give rise to more fruitful physics at their interface, while they face extreme difficulty in high-dimensional lattice matching. Here, we successfully demonstrate the non-Hermitian Weyl interface physics in complex synthetic parameter space, which is implemented in a loss-controlled silicon waveguide array. By establishing non-Hermitian Hamiltonian in the parameter space, new Weyl interfaces with distinct topological origins are predicted and experimentally observed in silicon waveguides. Significantly, our Letter exploits the non-Hermitian parameter to create the synthetic dimension by manipulating the non-Hermitian order, which successfully circumvents the difficulty in lattice matching for high-dimensional interfaces. The revealed rich topological Weyl interface states and their phase transitions in silicon waveguide platform further imply potentials in chip-scale photonics integrations.

Topological phononics arising from fluid-solid interactions

Nontrivial band topologies have been discovered in classical systems and hold great potential for device applications. Unlike photons, sound has fundamentally different dynamics and symmetries in fluids and solids, represented as scalar and vector fields, respectively. So far, searches for topological phononic materials have only concerned sound in either fluids or solids alone, overlooking their intricate interactions in “mixtures”. Here, we report an approach for topological phononics employing such unique interplay, and demonstrate the realization of type-II nodal rings, elusive in phononics, in a simple three-dimensional phononic crystal. Type-II nodal rings, as line degeneracies in momentum space with exotic properties from strong tilting, are directly observed through ultrasonic near-field scanning. Strongly tilted drumhead surface states, the hallmark phenomena, are also experimentally demonstrated. This phononic approach opens a door to explore topological physics in classical systems, which is easy to implement that can be used for designing high-performance acoustic devices.

Fluid-solid interaction, long investigated, is mostly neglected in topological acoustics. Here the authors find that it can give rise to intriguing topological phenomena in simple phononic crystals due to intrinsic differences between sound in fluid and solid.

Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal

Weyl points-topological monopoles of quantized Berry flux-are predicted to spread to Weyl exceptional rings in the presence of non-Hermiticity. Here, we use a one-dimensional Aubry-Andre-Harper model to construct a Weyl semimetal in a three-dimensional parameter space comprising one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a synthetic Weyl exceptional ring (SWER). The topology of the SWER is characterized by both its topological charge and non-Hermitian winding numbers. We experimentally observe the SWER and synthetic Fermi arc in a one-dimensional phononic crystal with the non-Hermiticity introduced by active acoustic components. Our findings pave the way for studying the high-dimensional non-Hermitian topological physics in acoustics.

Tracking Valley Topology with Synthetic Weyl Paths

Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.

Synthetic Topological Nodal Phase in Bilayer Resonant Gratings

The notion of synthetic dimensions in artificial photonic systems has received considerable attention as it provides novel methods for exploring hypothetical topological phenomena as well as potential device applications. Here, we present nanophotonic manifestation of a two-dimensional topological nodal phase in bilayer resonant grating structures. Using the mathematical analogy between a topological semimetal and vertically asymmetric photonic lattices, we show that the interlayer shift simulates an extra momentum dimension for creating a two-dimensional topological nodal phase. We present a theoretical model and rigorous numerical analyses showing the two nodal points that produce a complex gapless band structure and localized edge states in the topologically nontrivial region. Therefore, our results provide a practical scheme for producing high-dimensional topological effects in simple low-dimensional photonic structures.

Synthetic Three-Dimensional Z×Z_{2} Topological Insulator in an Elastic Metacrystal

We report a three-dimensional (3D) topological insulator (TI) formed by stacking identical layers of Chern insulators in a hybrid real-synthetic space. By introducing staggered interlayer hopping that respects mirror symmetry, the bulk bands possess an additional Z_{2} topological invariant along the stacking dimension, which, together with the nontrivial Chern numbers, endows the system with a Z×Z_{2} topology. A 4-tuple topological index characterizes the system's bulk bands. Consequently, two distinct types of topological surface modes (TSMs) are found localized on different surfaces. Type-I TSMs are gapless and are protected by Chern numbers, whereas type-II gapped TSMs are protected by Z_{2} bulk polarization in the stacking direction. Remarkably, each type-II TSM band is also topologically nontrivial, giving rise to second-order topological hinge modes (THMs). Both types of TSMs and the THMs are experimentally observed in an elastic metacrystal.

Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries

The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA-the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

Zero-Index Weyl Metamaterials

Depending on the geometry of their Fermi surfaces, Weyl semimetals and their analogs in classical systems have been classified into two types. In type-I Weyl semimetals (WSMs), the conelike spectrum at the Weyl point is not tilted, leading to a pointlike closed Fermi surface. In type-II WSMs, on the contrary, the energy spectrum around the Weyl point is strongly tilted such that the Fermi surface transforms from a point into an open surface. Here, we demonstrate, both theoretically and experimentally, a new type of (classical) Weyl semimetal whose Fermi surface is neither a point nor a surface, but a flat line. The distinctive Fermi surfaces of such semimetals, dubbed as type-III or zero-index WSMs, gives rise to unique physical properties: one of the edge modes of the semimetal exhibits a zero index of refraction along a specific direction, in stark contrast to type-I and type-II WSMs for which the index of refraction is always nonzero. We show that the zero-index response of such topological phases enables exciting applications such as extraordinary wave transmission.

Acoustic Realization of Quadrupole Topological Insulators

A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here, we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge, and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.

Exceptional cones in 4D parameter space

The notion of synthetic dimensions has expanded the realm of topological physics to four dimensional (4D) space lately. In this work, non-Hermiticity is used as a synthetic parameter in PT-symmetric photonic crystals to study the topological physics in 4D non-Hermitian synthetic parameter space. We realize a 3D exceptional hypersurface (EHS) in such 4D parameter space, and the degeneracy points emerge due to the symmetry of synthetic parameters. We further demonstrate the existence of exceptional degenerate points (EDPs) on the EHS that originates from the chirality of exceptional points (EPs), and the exceptional surface near EDPs behaves like a Dirac cone. We further show that a very narrow reflection plateau can be found near these EDPs, and their sensitivity towards the PT-symmetry breaking environmental perturbation can make these degeneracy points useful in optical sensing and many other nonlinear and quantum optical applications.

Hybrid Acoustic Topological Insulator in Three Dimensions

Topological insulators (TIs), featured by a symmetry-protected gapless surface Dirac cone(s) in their complete energy band gaps, have been extended from condensed-matter physics to classical bosonic systems in the last decade. However, acoustic TIs in three dimensions remain elusive because of a lack of a spin or polarization degree of freedom for longitudinal airborne sound. Here, we experimentally demonstrate a feasible way to hybridize an acoustic TI in three dimensions based on band inversion through a three-dimensional (3D) hybrid Dirac point (HDP). Such a 3D HDP, with linear dispersion in the layer plane while quadratic out of the layer, is distinct from a general point with linear dispersion in all directions. Interestingly, a single nearly gapless conical-like dispersion for acoustic surface states can be achieved at both zigzag and armchair interfaces, supporting robust sound transport. Our findings can serve as a tabletop platform for exploring unique acoustic applications based on the two-dimensional topological interfaces.