Higher-order Topological Insulators Research Articles

Higher-order topological insulators in three dimensions without crystalline counterparts

Higher-order topological insulators in three dimensions without crystalline counterparts

Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems.

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form similarity between Schrödinger equation and diffusion equation, research on higher-order topological insulators has been extended from condensed matter physics to thermal diffusion. Unfortunately, all the corner states of thermal higher-order topological insulator reside within the band gap. Another kind of corner state, which is embedded in the bulk states, has not been realized in pure diffusion systems so far. Here, we construct higher-dimensional Su-Schrieffer-Heeger models based on sphere-rod structure to elucidate these corner states, which we term "in-bulk corner states." Because of the anti-Hermitian properties of diffusive Hamiltonian, we investigate the thermal behavior of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviors of in-bulk corner state and in-gap corner state. Our results would open a different gate for diffusive topological states and provide a distinct application for efficient heat dissipation.

RKKY interaction in helical higher-order topological insulators

Abstract We theoretically investigate the RKKY interaction in helical higher-order topological insulators (HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms, exhibiting a decay with impurity spacing $z$ and oscillations with Fermi energy $\varepsilon_F$. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into the design of next-generation quantum devices based on the HOTIs.

Enhanced surrounding sound signal acquisition for arbitrary source location by the acoustic higher-order topological insulator

Enhanced surrounding sound signal acquisition for arbitrary source location by the acoustic higher-order topological insulator

Robust ultra-high-Q Fano resonance for topological corner and ring-cavity mode coupling in Kagome photonic systems

Corner and edge states in higher-order topological insulators provide new degrees of freedom for manipulating light propagation. Our research demonstrates that the topological waveguide coupled to the corner and edge states of the triangular cavity obtains a topological corner mode as narrow resonance and a topological ring-cavity mode as broad resonance, respectively. By adjusting the size of the dielectric column at the apex of the triangular cavity, the two modes can be coherently coupled at the same frequency position and obtain a high-Q Fano resonance. This Fano resonant has excellent robustness for unavoidable defects in the manufacturing process, paving the way for the design of high-performance lasers, switches, and other micro-nano integrated photonics devices.

Hermitian and non-hermitian higher-order topological states in mechanical metamaterials

Higher-order topological insulators exhibit clear hierarchical boundary states, providing an amazing platform for robust wave manipulations in mechanical or acoustic systems. Recently, this theory has been extended to non-Hermiticity-induced higher-order topology, which enables actively controllable topological transport. Nevertheless, most related studies focus on the non-Hermitian quadrupole topology, associated with the coexistence of negative and positive couplings to constitute a π-flux lattice, which hindered the realizations in classical wave systems. Here, we propose a novel tight-binding model without negative couplings, which supports non-Hermiticity-induced higher-order topological states. In the Hermitian case, the middle band gaps host the vanishing bulk polarization and the associated topology is dependent only upon the associated edge polarization. By introducing the external loss as non-Hermitian components, we reveal that therein the trivial structures can also host topological corner states, featured by the quantized nonzero edge polarizations in the biorthogonal basis. Furthermore, such a topological phase transition induced by non-Hermiticity can be realized for almost all of our lattices, except for the isotropic case where the middle band gaps never open. Basing on the theoretical design, we map the lattice models into the mechanical metamaterials to access the analogous higher-order topology in the elastic wave systems for both Hermitian and non-Hermitian physics. The simulated band structures match well with theoretical solutions. And the robust higher-order topological states are also identified. Our work paves the way to implement the non-Hermitian higher-order topology and offers the possibility for wave manipulations in non-Hermitian systems.

Corner states and particle trapping in waterborne acoustic crystals

Higher-order topological insulators exhibit intriguing capacity to confine energy on lower-dimensional boundaries owing to the unique bulk-boundary correspondence. Many potential practical applications of the higher-order states in classical wave systems have been proposed and achieved. In this work, we implement a second-order topological insulator in a waterborne acoustic crystal by drilling and grooving a copper plate based on a two-dimensional Su–Schrieffer–Heeger lattice with different intracell and intercell couplings. The far-field transmission spectrum and near-field pressure field distributions verify the existence of the one-dimensional edge states and zero-dimensional corner states in the bulk bandgap. Due to the highly localized edge and corner states, the polystyrene particles are trapped at the edges and corners by the acoustic gradient force. Our findings provide a good platform to manipulate underwater acoustic wave and may inspire topological acoustic applications.

Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions.

The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.

Photoinduced high-Chern-number quantum anomalous Hall effect from higher-order topological insulators

Photoinduced high-Chern-number quantum anomalous Hall effect from higher-order topological insulators

Observation of Higher-Order Nodal-Line Semimetal in Phononic Crystals.

Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature twofold linear crossing points in three-dimensional momentum space, 2D Fermi-arc surface states, and 1D hinge states. Higher-order nodal-point semimetals possessing Weyl points or Dirac points have been implemented. However, higher-order nodal-line or nodal-surface semimetals remain to be further explored in experiments in spite of many previous theoretical efforts. In this work, we realize a second-order nodal-line semimetal in 3D phononic crystals. The bulk nodal lines, 2D drumhead surface states guaranteed by Zak phases, and 1D flat hinge states attributed to k_{z}-dependent quadrupole moments are observed in simulations and experiments. Our findings of nondispersive surface and hinge states may promote applications in acoustic sensing and energy harvesting.

Topological edge and corner states in coupled wave lattices in nonlinear polariton condensates

Abstract Topological states have been widely investigated in different types of systems and lattices. In the present work, we report on topological edge states in double-wave (DW) chains, which can be described by a generalized Aubry-André-Harper (AAH) model. For the specific system of a driven-dissipative exciton polariton system we show that in such potential chains, different types of edge states can form. For resonant optical excitation, we further find that the optical nonlinearity leads to a multistability of different edge states. This includes topologically protected edge states evolved directly from individual linear eigenstates as well as additional edge states that originate from nonlinearity-induced localization of bulk states. Extending the system into two dimensions (2D) by stacking horizontal DW chains in the vertical direction, we also create 2D multi-wave lattices. In such 2D lattices multiple Su–Schrieffer–Heeger (SSH) chains appear along the vertical direction. The combination of DW chains in the horizonal and SSH chains in the vertical direction then results in the formation of higher-order topological insulator corner states. Multistable corner states emerge in the nonlinear regime.

Quartic-root higher-order topological insulators on decorated three-dimensional sonic crystals

The square-root operation provides a new scheme to create topological phases with unconventional spectrum properties. With the square-root operation, the square-root topological insulators can support paired topological boundary states in two bulk gaps, and the mechanism of square-root has been generalized to 2n-root topological insulators. In this study, we describe the acoustic realization of third-order quartic-root topological insulators based on the original three-dimensional (3D) square-root sonic crystals. By inserting extra sites into the 3D square-root lattice, we can renormalize the coupling parameters and obtain multiple topological boundary states in different bulk gaps with distinct phase profiles. The topological origin is clearly elucidated with the direct sum relation for the 3D quartic-root lattice. We further validate the robustness of the corner states under random bulk disorder and show the diversified localizations of topological edge states at distinct frequencies on different-shaped 3D sonic crystals. Our work extends the quartic-root topological states into a 3D acoustic system and may find potential applications in multi-frequency acoustic devices.

Observation of Topological Corner State Arrays in Photonic Quasicrystals

AbstractRecently, the studies of topological corner states (TCSs) have been extended from crystals to quasicrystals, which are referred to as higher‐order topological quasicrystalline insulators (HOTQIs). However, the TCSs of complete quasi‐periodic structure in photonic systems have yet to be demonstrated. Moreover, there is only one TCS in each corner region in higher‐order topological insulators (HOTIs). Increasing the number of TCS is expected to increase the application potential of TCSs. In this work, HOTQIs in photonic systems are experimentally observed. It is found that HOTQIs possess TCS arrays, and each TCS array contains several TCSs. Furthermore, the universal theoretical framework of the multimer analysis method is improved, and the difference in the average charge density is proposed as a real‐space topological index. These results will open up new ideas for investigating highly integrated, multi‐region localized TCSs and are expected to provide new ways to explore topological phenomena and the applications of photonic quasicrystals.

Vortex solitons in topological disclination lattices

Abstract The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

Programmable integrated photonics for topological Hamiltonians

A variety of topological Hamiltonians have been demonstrated in photonic platforms, leading to fundamental discoveries and enhanced robustness in applications such as lasing, sensing, and quantum technologies. To date, each topological photonic platform implements a specific type of Hamiltonian with inexistent or limited reconfigurability. Here, we propose and demonstrate different topological models by using the same reprogrammable integrated photonics platform, consisting of a hexagonal mesh of silicon Mach-Zehnder interferometers with phase shifters. We specifically demonstrate a one-dimensional Su-Schrieffer-Heeger Hamiltonian supporting a localized topological edge mode and a higher-order topological insulator based on a two-dimensional breathing Kagome Hamiltonian with three corner states. These results highlight a nearly universal platform for topological models that may fast-track research progress toward applications of topological photonics and other coupled systems.

Model-free characterization of topological edge and corner states in mechanical networks

Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust responses in wave guiding, sensing, computation, and filtering. However, determining whether a mechanical structure is topologically nontrivial and features topologically protected modes has hitherto relied on theoretical models. This strong requirement has limited the experimental and practical significance of topological mechanics to laboratory demonstrations. Here, we introduce and validate an experimental method to detect the topologically protected zero modes of mechanical structures without resorting to any modeling step. Our practical method is based on a simple electrostatic analogy: Topological zero modes are akin to electric charges. To detect them, we identify elementary mechanical molecules and measure their chiral polarization, a recently introduced marker of topology in chiral phases. Topological zero modes are then identified as singularities of the polarization field. Our method readily applies to any mechanical structure and effectively detects the edge and corner states of regular and higher-order topological insulators. Our findings extend the reach of chiral topological phases beyond designer materials and allow their direct experimental investigation.

Observation of a Higher-Order End Topological Insulator in a Real Projective Lattice.

The modern theory of quantized polarization has recently extended from 1D dipole moment to multipole moment, leading to the development from conventional topological insulators (TIs) to higher-order TIs, i.e., from the bulk polarization as primary topological index, to the fractional corner charge as secondary topological index. The authors here extend this development by theoretically discovering a higher-order end TI (HOETI) in a real projective lattice and experimentally verifying the prediction using topolectric circuits. A HOETI realizes a dipole-symmetry-protected phase in a higher-dimensional space (conventionally in one dimension), which manifests as 0D topologically protected end states and a fractional end charge. The discovered bulk-end correspondence reveals that the fractional end charge, which is proportional to the bulk topological invariant, can serve as a generic bulk probe of higher-order topology. The authors identify the HOETI experimentally by the presence of localized end states and a fractional end charge. The results demonstrate the existence of fractional charges in non-Euclidean manifolds and open new avenues for understanding the interplay between topological obstructions in real and momentum space.

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System.

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

Higher-order topological states in dual-band valley sonic crystals

As a quantum state of frequency extrema in the momentum space of acoustic systems, sonic valley pseudospin provides a new degree of freedom for controlling acoustic waves. Higher-order topological insulators (HOTIs) have extended the traditional bulk-edge correspondence principle and are a crucial concept for classic wave regulation. However, HOTIs in valley sonic crystals (VSCs) only appear in a single bandgap, which limits the multi-frequency selectivity of the corner state and is not conducive to the design of multi-frequency acoustic communication devices. Here, we demonstrate “Y-shaped” acoustic crystals with C3 symmetry that form a double-band VSC, and the topological phase transitions in both low- and high-frequency band gaps coincide. We realize theoretically and experimentally higher-order states in dual-band valley sonic crystals. Our work enriches the application of HOTIs in acoustic multi-frequency regulatory systems and provides different avenues for designing of multi-band acoustic devices.

Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4

The notion of topological insulators (TIs), characterized by an insulating bulk and conducting topological surface states, can be extended to higher-order topological insulators (HOTIs) hosting gapless modes localized at the boundaries of two or more dimensions lower than the insulating bulk. In this work, by performing high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements with submicron spatial and spin resolution, we systematically investigate the electronic structure and spin texture of quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the bulk-state-dominant spectra on the (001) surface, we observe gapped surface states on the (100) surface, whose dispersion and spin-polarization agree well with our ab-initio calculations. Moreover, we reveal in-gap states connecting the surface valence and conduction bands, which is a signature of the hinge states inside the (100) surface gap. Our findings provide compelling evidence for the HOTI phase of Bi4Br4. The identification of the higher-order topological phase promises applications based on 1D spin-momentum locked current in electronic and spintronic devices.