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The body–boundary correspondence refers to the relationship between the body and boundary states of topological insulators (TIs). In TIs, the presence of boundary states is connected to the bulk topological properties of the material. The topology can be identified by studying the energy of the topological modes within the bulk bandgap. However, not all topological materials exhibit boundary states within the insulating energy gap. In many cases, the presence of boundary states can be hidden or masked by the bulk energy bands, making it difficult to measure TIs. Recent experiments have shown that defects, which are commonly found in crystalline materials, can be used as probes to explore higher-order topologies that have been recently realized on various platforms. These defects can generate fractional charges and stable bound states in the dispersion region, allowing us to observe the clear body–disclination correspondence. We have performed simulations using a coupled acoustic cavity system with C3 and C5 symmetries to investigate the body–disclination correspondence in topological crystal insulators (TCIs) in the field of acoustics. Simulation and theoretical results have demonstrated that defects such as disclinations can be used to probe higher-order topologies that were previously unobservable in three-dimensional structures. This approach allows us to detect fractional mode charges and stable bound states, which are crucial for understanding the topological nature of TCIs. Our work demonstrates the potential of using disclination defects to study the intricate relationship between the body and boundary states in topological materials, particularly in the context of acoustics. [ABSTRACT FROM AUTHOR]

The measurement of topological insulators is usually achieved by measuring spectra, which is inadequate in higher-order topological insulators because the separation of bandgaps may be blurred, such as body boundaries and corner state hybridization, and the above measurement requires that the energy of the topological mode must be located in the bulk bandgap to be measured. Recent experiments have shown a strong relationship between the fractional mode charge and the location of the Wannier center in the crystal body. The fractional quantization of the corner charge originates from the filling anomaly, and the fractional mode charge can be calculated from experimental measurements of the local density of states to describe the topological state of the system, which has been demonstrated in optical systems. We have achieved a similar effect in acoustics by utilizing a coupled acoustic-cavity system featuring C3, C4, and C6 symmetries for simulation. Furthermore, we extended our study to 3D third-order topological crystalline insulators to validate the fractional-corner charge approach. The simulation and theoretical results demonstrate that the fractional mode charge can clearly identify the high-order topology, even without gap states. [ABSTRACT FROM AUTHOR]

Beyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics. Though non-Hermitian physics has contributed toward the advance of research in quantum, electronic and classical systems, previous work focused on zero- or one-dimensional systems. Here, the authors report higher-order non-Hermitian skin effects in a 2D acoustic higher-order topological insulator. [ABSTRACT FROM AUTHOR]

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 confidence in 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. [ABSTRACT FROM AUTHOR]

Topological insulators (TIs) can host an insulating gapped bulk with conducting gapless boundary states in lower dimensions than the bulk. To date, various kinds of classical wave TIs with gapless symmetry-protected boundary states have been discovered, promising for the efficient confinement and robust guiding of waves. However, for airborne sound, an acoustic analogue of a three-dimensional TI has not been achieved due to its spinless nature. Here, we experimentally demonstrate a three-dimensional topological acoustic crystal with pseudospins using bilayer chiral structures, in which multi-order topological bandgaps are generated step by step via elaborately manipulating the corresponding spatial symmetries. We observe acoustic analogues of 1st-order (two-dimensional gapless surface Dirac cones) and 2nd-order (one-dimensional gapless hinge Dirac dispersion) TIs in three dimensions, supporting robust surface or hinge sound transport. Based solely on spatial symmetry, our work provides a route to engineer the hierarchies of TIs and explore topological devices for three-dimensional spinless systems. An acoustic analogue of a three-dimensional topological insulator (TI) has not been achieved, despite various realizations in other kinds of TIs. Here, the authors report a three-dimensional multi-order TI in an acoustic bilayer chiral structure, with robust surface or hinge sound transport. [ABSTRACT FROM AUTHOR]

Topological phases of matter with robust edge states have revolutionized the fundamental intuitions for wave control. The recent development of higher-order topological insulators (HOTIs) realizes even lower dimensional topological states that enable versatile wave manipulations (e.g., light imaging). However, in conventional HOTIs, the topological states are usually protected by certain crystalline symmetries and therefore bounded at specific locations, hindering their applications in modern digital ears, which often prefer tunability and reconfigurability. Here, we report the reconfigurable light imaging based on topological corner states and anti-chiral edge states in a two-dimensional (2D) photonic HOTI with a honeycomb lattice of yttrium iron garnet (YIG, a ferrite material) rods. Sublattices A and B are applied with magnetic fields in opposite directions, which realize the so-called modified Haldane model that hosts anti-chiral edge modes. By further breaking the lattice's inversion symmetry via adjusting the radii of A and B rods, topological edge states with valley degrees of freedom emerge, which not only exhibit valley-dependence but also surprisingly show anti-chiral behaviors. In the valley edge gap, which is of nontrivial higher-order topology, corner states appear. With different combinations of corner states and anti-chiral edge states, versatile reconfigurable light imaging can be realized. As examples, a multiplexing waveguide-resonator device, a pine tree imaging that can be lit up or put out at will and selective imaging for partial objects in a two-heart pattern are demonstrated. The proposed HOTI shows high potential in future intelligent devices with exciting tunable and reconfigurable functions, which may inspire a wide range of applications such as topological switching, imaging processing, and nonreciprocal integrated photonics. [ABSTRACT FROM AUTHOR]

Exploring new topological materials with large topological nontrivial bandgaps and simple composition is attractive for both theoretical investigation and experimental realization. Recently, alpha tin (α‐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, freestanding α‐Sn is only stable below 13.2 °C. Herein, a series of high‐quality α‐Sn films with different thicknesses are 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 remain fully strained up to 400 nm, proving the strain effect from the substrate. Remarkably, the single‐crystalline α phase can persist up to 170 °C for the 20 nm thick sample. The critical temperature where the α phase disappears decreases as the film thickness increases, showing that the thermal stabilization can be engineered by varying the α‐Sn thickness. A plastic flow model considering work hardening is introduced to explain this dependence, assuming that the strain relaxation and the phase transition occur successively. This enhanced thermal stability is prerequisite for aforementioned room‐temperature characterization and practical application of this material system. [ABSTRACT FROM AUTHOR]

Time-reversal symmetry (TRS) of electrons is associated with an anti-unitary operator with T 2 = − 1 , which induces Kramers degeneracy and plays an important role in realizing the quantum spin Hall effect (QSHE). By contrast, TRS of photons is described by T b 2 = 1 . We point out that due to this difference, TRS is not the necessary condition for the construction of the photonic analogue of the QSHE. Instead, by constructing an artificial pseudo TRS T p with T p 2 = − 1 in a photonic system, one can realize the photonic Kramers degeneracy and a pair of topological protected edge states, a photonic analogue of the QSHE. Specifically, by retrieving the optical parameters of materials with the pseudo TRS, we propose a photonic topological insulator (PTI) utilizing a pair of double-degenerate transverse electric (TE) and transverse magnetic (TM) polarizations to mimic the spin up and down states of the electron. We demonstrate that the unidirectional polarization-dependent transportation of TE and TM edge states can be realized in this system based on computer simulations. For all possible symmetry types, we check the robustness of these topological states by using a complete set of impurities, including three Pauli matrices and one complex conjugate operator. The results show that the PTI is protected by the pseudo TRS T p . In general, an arbitrary pair of optical polarizations on the Bloch sphere can be utilized to construct photonic pseudospin states and the PTI. Our findings confirm the physical meaning of the pseudo TRS and may provide guidance for future PTI designs. [ABSTRACT FROM AUTHOR]

Transition metal compounds with quasi-two-dimensional structure demonstrate a series of un-precedent quantum phases, such as topological insulator, topological phase transition under thermal/pressure stimuli, which is attributed to delicate interplay among interlayer coupling, spin-orbit coupling and stoichiometry. Here, Cu 2 TlSe 2 and Cu 2 TlTe 2 crystals were successfully synthesized by Bridgeman method. Highly crystalline quality of these samples is verified by X-ray diffraction and microstructural characterization. Temperature-dependent-Hall-resistivity shows that Cu 2 TlSe 2 is hole-like and Hall resistivity is in-sensitive to temperature; while Hall resistivity of Cu 2 TlTe 2 is positive at room temperature and change to negative at 30 K. Combined experimental results and electronic band structures calculated by first-principles method, it is revealed that Cu 2 TlSe 2 is a metal, but Cu 2 TlTe 2 is a semi-metal. This work demonstrates the rich physical phases of layered transition metal compounds under the interplay among interlayer coupling, spin-orbit coupling and stoichiometry. [ABSTRACT FROM AUTHOR]