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Spin and orbital angular momenta are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the orbital angular momentum ubiquitous to any scalar field. Common wisdom treats these two degrees of freedom as distinct and independent principles to manipulate wave propagations. Here, we demonstrate their synergy. This is achieved by introducing two orthogonal $p$-orbitals as eigenbases, whose spatial modal features are exploited to generate orbital angular momenta and the associated orbital orientations provide means to simultaneously manipulate polarizations. Through periodic modulation and directional coupling, we realize a full cyclic evolution of the synchronized and synergized spin-orbital angular momenta. Remarkably, this evolution acquires a nontrivial geometric phase, leading to its representation on a M\"obius strip. Experimentally, an acoustic cavity array is designed, whose dipole resonances precisely mimic the $p$-orbitals. The acoustic waves, uniquely, see the pressure (scalar) field as a spatial feature and carry an intrinsic polarization defined by the velocity (vector) field, serving as an ideal platform to observe the synergy of spin and orbital angular momenta. Based on such a property, we further showcase a spin-orbital-Hall effect, highlighting the intricate locking of handedness, directionality, spin density and spatial mode profile. Our study unveils a fundamental connection between spin and orbital angular momenta, promising avenues for novel applications in information coding and high-capacity communications.

Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk Fermi arcs. Recent studies further show that non-Hermiticity can fundamentally change the topological band theory, leading to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed in one-dimensional (1D) systems. However, in higher dimensions, these non-Hermitian effects remain unexplored in experiments. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional (2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery acoustic resonators, we realize a spinful 2D higher-order topological insulator (HOTI) where the spin-up and spin-down states are emulated by the anti-clockwise and clockwise modes, respectively. We find that the non-Hermiticity drives wave localizations toward opposite edge boundaries depending on the spin polarizations. More interestingly, for finite systems with both edge and corner boundaries, the higher-order non-Hermitian skin effect leads to wave localizations toward two corner boundaries for the bulk, edge and corner states in a spin-dependent manner. We further show that such a non-Hermitian skin effect enables rich wave manipulation through the loss configuration in each unit-cell. The reported spin-dependent, higher-order non-Hermitian skin effect reveals the interplay between higher-order topology and non-Hermiticity, which is further enriched by the spin degrees of freedom. This unveils a new horizon in the study of non-Hermitian physics and the design of non-Hermitian metamaterials.

Waveguides and resonators are core components in the large-scale integration of electronics, photonics, and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e., no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing, and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting, and intense wave-matter interactions, using phonons, photons, or even electrons. The present work further enhances the confidence of using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime., Comment: 46 pages, 6 figures in main text, 16 figures in Supplementary Materials

Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.

Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect of light, where electromagnetic waves propagate along surfaces of samples with strong spin-momentum locking, paves the way for achieving topologically protected photonic spin transport. Recently, the conventional bulk-edge correspondence of the band topology has been extended to higher-order cases that enables the explorations of topological states with codimensions larger than 1 such as hinge and corner states. Here, for the first time, we demonstrate a higherorder quantum spin Hall effect of light by utilizing an all-dielectric C6v-symmetric photonic crystal. We observe corner states with opposite pseudospin polarizations at different corners owing to nontrivial higher-order topology and finite spin-spin coupling. By applying the spin-polarized excitation sources, we can selectively excite the corner states at different spatial positions through spin-momentum-locked decaying edge states, resembling the quantum spin Hall effect in a higher-order manner. Our work which breaks the barriers between the spin photonics and higher-order topology opens the frontiers for studying lower-dimensional spinful classical surface waves and supports explorations in robust communications., Comment: 24 pages, 4 figures

Exploring new topological materials with large topological nontrivial bandgaps and simple composition is attractive for both theoretical investigation and experimental realization. Recently alpha tin ({\alpha}-Sn) has been predicted to be such a candidate and it can be tuned to be either a topological insulator or a Dirac semimetal by applying appropriate strain. However, free-standing {\alpha}-Sn is only stable below 13.2 {\deg}C. In this study, a series of high-quality {\alpha}-Sn films with different thicknesses have been successfully grown on InSb substrates by molecular beam epitaxy (MBE). Confirmed by both X-ray diffraction (XRD) and reciprocal space mapping (RSM), all the films remained fully strained up to 4000 {\AA}, proving the strain effect from the substrate. Remarkably, the single-crystalline {\alpha} phase can persist up to 170 {\deg}C for the 200 {\AA} thick sample. The critical temperature where the {\alpha} phase disappears decreases as the film thickness increases, showing the thermal stabilization can be engineered by varying the {\alpha}-Sn thickness. A plastic flow model taking the work hardening into account is introduced to explain this dependence, assuming the strain relaxation and the phase transition occur successively. This enhanced thermal stability is prerequisite for above room-temperature characterization and application of this material system., Comment: 21 pages, 4 figures, 1 table

The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with $\pi$-fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux, using 2D sonic crystals with $p4gm$ and $p2gg$ symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate, gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, (iii) quantized Wannier band polarizations in these Wannier sectors. Remarkably, the protective glide symmetries are well-preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering., Comment: 5+ pages 4 figures

Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond the conventional topological paradigms. Here, we discover experimentally that the nonsymmorphic $p4g$ acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, while the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexing topological phenomena and to reveal a topological transition triggered by the geometry-transition from the $p4g$ group to the $C_{4v}$ group which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates an instance that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions., Comment: 5 figures. Accepted by Nature Communications

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not been found in photonic systems yet. In this article, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically non-trivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily-fabricated structure of the photonic crystals, we can realize different topological phases with unique topological boundary states straightforwardly. Our result can be generalized to higher dimensions and provides unprecedented venues for higher-order photonic topological insulators and semimetals., Comment: 6 pages, 6 figures, Phys. Rev. B 2018

Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of topological node-lines in three-dimensional mechanical metacrystals with ribbon- or drumhead-like surface states. These two-dimensional topological surface states offer unprecedented, robust subwavelength confinement of elastic waves. Design principles for topological mechanical metamaterials, from both material and symmetry aspects, are unveiled and connected to fundamental conservation laws and nonsymmorphic space group. Our study paves the way toward the synergy between three-dimensional mechanical metamaterials and topological wave dynamics.

The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted WTe$_{1.98}$ crystals. Quantitatively, $C_w$ , a coefficient representing intensity of ABJ anomaly, along a- and b-axis of WTe$_{1.98}$ are 0.030 and 0.051 T$^{-2}$ at 2 K, respectively. We found that temperature-sensitive ABJ anomaly is attributed to topological phase transition from type-II Weyl semimetal to trivial semimetal, which is verified by first-principles calculation using experimentally determined lattice parameters at different temperatures. Theoretical electrical transport study reveals that observation of ansotropic ABJ both along a- and b-axis in WTe$_{1.98}$ is attributed to electrical transport in the quasi-classical regime. Our work may suggest that electron-doped WTe$_2$ is an ideal playground to explore the novel properties in type-II Weyl semimetals., Comment: 20 pages, 5 figures, 1 table

Recently, the extremely large magnetoresistance observed in transition metal telluride, like WTe$_2$, attracted much attention because of the potential applications in magnetic sensor. Here we report the observation of extremely large magnetoresistance as 3.0$\times$10$^4$ % measured at 2 K and 9 T magnetic field aligned along [001]-ZrSiS. The significant magnetoresistance change (~1.4$\times$10$^4$ %) can be obtained when the magnetic field is titled from [001] to [011]-ZrSiS. These abnormal magnetoresistance behaviors in ZrSiS can be understood by electron-hole compensation and the open orbital of Fermi surface. Because of these superior MR properties, ZrSiS may be used in the novel magnetic sensors., Comment: 18 pages, 5 figures, 21 references

We report an atomic-scale characterization of ZrTe$_5$ by using scanning tunneling microscopy. We observe a bulk bandgap of ~80 meV with topological edge states at the step edge, and thus demonstrate ZrTe$_5$ is a two dimensional topological insulator. It is also found that an applied magnetic field induces energetic splitting and spatial separation of the topological edge states, which can be attributed to a strong link between the topological edge states and bulk topology. The perfect surface steps and relatively large bandgap make ZrTe$_5$ be a potential candidate for future fundamental studies and device applications., Comment: 11 pages, 3 figures