Conventional Topological Insulators Research Articles

Engineering Higher-Order Topological Confinement via Acoustic Non-Hermitian Textures.

Higher-order topological insulators are a newly unveiled category of topological materials, distinguished by their exceptional characteristics absent in conventional topological insulators, e.g., 1D hinge states, or zero-dimensional corner states, for instance. Adding attenuating or amplifying components manifest even richer and more intricate non-Hermitian topological properties. While losses, for the most part, come for free, decorating topological systems with the gain counterpart poses significant challenges. Here, a non-Hermitian second-order topological insulator (SOTI) is constructed for a sonic demonstration, by bestowing a cavity-based lattice both with electro-thermoacoustic gain and loss. The inner cavity walls are decorated with electrically biased carbon nanotube films to be able to manipulate spatially and in strength, a non-Hermitian response at will. These measurements demonstrate that this flexibility allows us to design highly unconventional interface and corner confining topologies by decisively engineering gain and loss textures within the unit cell. It is foreseen that the advances may enable new avenues for energy harvesting and fundamental understanding in condensed matter and classical topologicalphysics.

Topological edge states of massless fermions with nonquantized and zero Berry phases

We investigate the bulk-boundary correspondence for massless Dirac fermions in α−T3 lattice where the Berry phase can be continuously tuned from π (graphene) to 0 (T3 or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by the unitary transformation of the Hamiltonian, which maps an α−T3 zigzag ribbon (ZR) onto a stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the topological invariant is manifested by the azimuthal winding number on the Bloch sphere. Particularly, T3 ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to conventional topological insulators, the gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition. Published by the American Physical Society 2024

Observation of multiple topological bound states in the continuum in the photonic bilayer trimer lattice

A topological bound state in the continuum (TBIC) is a novel topological phase that has attracted significant attention. Different from conventional topological insulators (TIs), where boundary states reside within gaps, TBICs can support unconventional boundary states that remain isolated from the surrounding bulk states. In this work, we experimentally demonstrate multiple TBICs in photonic bilayer trimer lattices using femtosecond laser writing technology. By modulating the interlayer coupling between two trimer chains, we observe the emergence of two distinct types of TBICs. Moreover, we experimentally achieve the coexistence of in-gap topological states and TBICs and demonstrate the transformation between them. Our work unveils new insights into the flexible construction of TBICs, and this method can be easily applied to other one-dimensional topological structures, offering promising avenues for further research.

Edge Zeros and Boundary Spinons in Topological Mott Insulators.

We use a real-space slave-rotor theory of the physics of topological Mott insulators, using the Kane-Mele-Hubbard model as an example, and show that a topological gap in the Green function zeros corresponds to a gap in the bulk spinon spectrum and implies a gapless band of edge zeros and a spinon edge mode. We then consider an interface between a topological Mott insulator and a conventional topological insulator showing how the spinon edge mode of the topological Mott insulator combines with the spin part of the conventional electron topological edge state, leaving a non-Fermi liquid edge mode described by a gapless propagating holon and gapped spinon state. Our work demonstrates the physical meaning of Green function zeros and shows that interfaces between conventional and Mott topological insulators are a rich source of new physics.

Flexo-photovoltaic effect in strained bismuth telluride thin films without substrate bending under light irradiation

Bismuth telluride (Bi2Te3) is gaining increasing attention as a material that exhibits flexo-photovoltaic effect in the infrared region, in addition to conventional thermoelectric materials and topological insulators. However, the flexo-photovoltaic effect is observed only when strains are applied to the Bi2Te3 thin films by bending the substrates. To enhance the versatility of the flexo-photovoltaic effect, in this study, Bi2Te3 thin films were sputtered onto a flexible substrate under a pre-curved condition, and strains were induced when the films were flattened. The crystal orientation and strains in the Bi2Te3 thin films were affected by the pre-curved conditions. The Bi2Te3 thin film deposited using a concave pre-curved condition exhibited an output voltage increase of approximately 15 % compared with the film deposited under a flat condition. This discovery suggests that strained Bi2Te3 thin films can efficiently produce an output voltage under light irradiation without requiring a p–n junction, making them suitable for various photodetector applications.

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.

Hybrid plasmonic valley-Hall topological insulators

Abstract The emerging field of photonic topological insulators offers promising platforms for high-performance optical communication, computing, and sensing. However, conventional photonic topological insulator designs typically operate within the diffraction limit due to their dielectric nature. This limitation imposes constraints on device miniaturization, reduces light–matter interaction, and decreases overall device sensitivity. Introducing a new valley-Hall hybrid plasmonic topological insulator, we overcome this limitation by exploiting the coupling of surface plasmon oscillations with the optical modes of a dielectric photonic crystal, allowing for sub-diffraction vertical confinement of light. Deep-subwavelength chiral edge states can, therefore, be generated and robustly guided along disordered Z-shaped topological boundaries with much lower propagation loss compared to purely plasmonic platforms. Such extreme manipulation of light on an integrated chip platform maximizes light–matter interaction and opens the door for truly compact and efficient optical modulators, molecular sensors, and next-generation nanophotonic and quantum devices.

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.

A potential candidate material for quantum anomalous Hall effect: Heterostructures of ferromagnetic insulator and graphene

Discovery of novel topological materials have motivated tremendous research owing to their peculiar energy bands and potential fundamental and practical prospects. In contrast to conventional nonmagnetic topological insulators (TIs), new type of magnetic TIs, such as Cr2Ge2Te6, revealed a quantum Hall effect (QHE) at zero magnetic field. The phenomenon is called anomalous QHE. In the magnetic TIs showing QAHE, the interaction of spontaneous magnetism with conducting surface states opens an insulating band gap at the Dirac points by breaking the time-reversal symmetry. In contrast to inducing the phenomenon of QHE through spontaneous magnetism by chemical doping, the alternative suitable option is the heterostructure engineering of 2D Dirac materials with semiconductor magnetic insulators. In this study, we first time investigate the phenomenon of QAHE in semiconducting magnetic insulator Cr2Ge2Te6 by proposing its bulk and monolayer heterostructure with graphene by the first-principles calculations. We employed density functional theory to compute electronic properties of Cr2Ge2Te6 and its heterostructure with graphene. The exchange-correlation in view of meta-generalized gradient approximations with tight binding method reveal the results for bulk Cr2Ge2Te6 are close to the experimental values. The maximum achieved energy gap in the heterostructure is up to 5 meV.

Wide edge state supercontinuum in a Floquet–Lieb topological photonic insulator

Conventional topological photonic insulators typically have narrow nontrivial band gaps truncated by broad dispersive bulk bands, resulting in limited edge mode transmission bandwidths that can be exploited for potential applications. Here, we demonstrate a Floquet–Lieb topological photonic insulator with all flat bands that can support continuous edge mode transmission across multiple Floquet–Brillouin zones. This supercontinuum of edge states results from the coexistence and orthogonality of the localized flat-band modes and the edge states, allowing for continuous excitation of the latter without scattering into the bulk modes. Moreover, we show that these flat bands are perfectly immune to random variations in the on-site potential, regardless of how large the perturbations are, thus ensuring complete robustness of the edge modes to this type of disorder. We realized Floquet–Lieb insulators using 2D microring resonator lattices with perfect nearest-neighbor couplings. Transmission measurements and direct imaging of the scattered light distributions showed an edge mode supercontinuum spanning more than three microring free spectral ranges. The proposed Floquet–Lieb insulator can potentially be used to realize topological photonic devices with wide bandwidths and super robustness for applications in integrated quantum photonics and programmable photonic circuits.

Pseudospin Polarized Dual-Higher-Order Topology in Hydrogen-Substituted Graphdiyne.

Although the topological band theory is applicable to both Fermionic and bosonic systems, the same electronic and phononic topological phases are seldom reported in one natural material. In this work, we show the presence of a dual-higher-order topology in hydrogen-substituted graphdiyne (H-GDY) by first-principles calculations. The intriguing enantiomorphic flat-bands are realized in both electronic and phononic bands of H-GDY, which is confirmed to be an organic 2D second-order topological insulator (SOTI). Most importantly, we found that the topological corner states are pseudospin polarized in H-GDY, exhibiting a clockwise or counterclockwise texture perpendicular to the radial direction. Our results not only identify the existence of the dual-higher-order topology in covalent organic frameworks but also uncover a unique pseudospin polarization-coordinate locking relation, further extending the well-known spin-momentum locking relation in conventional topological insulators.

Induced superconductivity in the two-dimensional topological insulator phase of cadmium arsenide

Hybrid structures between conventional, s-wave superconductors, and two-dimensional topological insulators (2D TIs) are a promising route to topological superconductivity. Here, we investigate planar Josephson junctions fabricated from hybrid structures that use thin films of cadmium arsenide (Cd3As2) as the 2D TI material. Measurements of superconducting interference patterns in a perpendicular magnetic field are used to extract information about the spatial distribution of the supercurrent. We show that the interference patterns are distinctly different in junctions with and without mesa-isolation. In mesa-defined junctions, the bulk of the 2D TI appears to be almost completely shunted by supercurrent flowing along the edges, whereas the supercurrent is much more uniform across the junction when the Cd3As2 film extends beyond the device. We discuss the possible origins of the observed behaviors.

Acoustic graphyne: A second-order real Chern topological insulator

Graphyne has recently attracted much attention since it is an important derivative of graphene with unique topological properties. Although graphyne is not a conventional topological insulator because of its weak spin–orbit coupling, it is a real Chern topological insulator with the higher-order topology. However, it lacks a realistic model. Here, we propose a schedule to realize acoustic graphyne. By introducing negative coupling to simulate the carbon–carbon triple bond, we realize the transition from trivial to higher-order topological phases, characterized by real Chern numbers. These topologically protected corner states are achieved in a finite-size sample, and the condition for their existence is discussed. Our research extends the concept of real Chern insulators and provides a platform for studying the topological properties of graphene-like structural compounds.

Supersymmetric quantum mechanics of continuous topological insulators

In this paper, we construct a class of quantum systems in a space continuum inspired by results from topological insulator physics. Instead of adding spin–orbit coupling terms suggested by time-reversal invariance as in conventional topological insulators, the terms [Formula: see text] are determined using supersymmetry as a starting point. This procedure not only restricts the number of possible continuous topological insulators models, but also provides a systematic way to find new continuous topological insulators models. Some explicit quantum mechanical examples are discussed and applications to dark matter physics are also outlined.

Large spin hall conductivity in low-symmetry semiconductor ZrSe3

Spin-orbit torques (SOTs) in two-dimensional (2D) transition-metal dichalcogenides (TMDs) based on magnetic heterostructures have drawn extensive attentions owning to their potential applications in spintronic devices. Here, we investigated the current-induced SOTs in ZrSe3, which is a 2D van der Waals semiconductor characterized by both strong spin-orbit coupling and broken crystal symmetry. A large SOT efficiency along with an out-of-plane damping-like torque is achieved, when the charge current is applied along the low symmetry crystal axis of ZrSe3. Significantly, the SOT efficiency we detected from ZrSe3 (7.6 nm)/ Py(10 nm) device is up to 2.67, corresponding to a large spin Hall conductivity of 377.1 × 103ℏ/2e (Ω·m)−1. Such a large spin Hall conductivity is superior to most of the conventional heavy metals, TMDs and topological insulators. Thickness dependence study further demonstrates the main contribution to the large SOTs is bulk spin Hall effect in ZrSe3. Combining the notable out-of-plane damping-like SOT with high spin Hall conductivity, our study provides a new strategy for low-power SOT devices based on 2D semiconductors.

Disorder-induced topological phase transition in HgCdTe crystals

Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced \emph{uncorrelated} disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than it is expected for conventional 3D topological insulators. Our theoretical results can be also applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb and their ternary alloys InAsSb.

Second-order topological insulator in periodically driven optical lattices.

The higher-order topological insulator (HOTI) is a new type of topological system which has special bulk-edge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI with ultracold atoms in optical lattices. With the combination of periodically spin-dependent driving of the superlattices and a long-range coupling term, a Floquet second-order topological insulator with four zero-energy corner states emerges, whose Wannier bands are gapless and exhibit interesting bulk topology. Furthermore, the nearest-neighbor anisotropic coupling term also induced other intriguing topological phenomena, e.g. non-topologically protected corner states and topological semimetal for two different types of lattice structures respectively. Our scheme may give insight into the construction of different types of higher-order topological insulators in synthetic systems. It also provides an experimentally feasible platform to research the relations between different types of topological states and may have a wide range of applications in future.

Zeros of Green functions in topological insulators

This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.

Acoustic Realization of Surface-Obstructed Topological Insulators.

Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bulk and surface band gaps, as a direct manifestation of the higher-order band topology. Together with comparative measurements for the trivial and phase-transition-point insulators, our experimental data conclusively evidence the unique bulk-boundary physics for the surface-obstructed band topology. That is, the topological phase transition is determined by the closure of the surface gap, rather than by closing the bulk gap. Our study might spur on new activities to deepen the understanding of such elusive topological phases.

Phononic real Chern insulator with protected corner modes in graphynes

Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons in 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, we find that phonons in both graphdiyne and $\gamma$-graphyne exhibit a second-order topology, which belongs to the specific case known as real Chern insulator. We identify the nontrivial phononic band gaps, which are characterized by nontrivial real Chern numbers enabled by the spacetime inversion symmetry. The protected phonon corner modes are verified by the calculation on a finite-size nanodisk. Our study extends the scope of higher-order topology to phonons in real materials. The spatially localized phonon modes could be useful for novel phononic applications.