Geometric control of topological dynamics in a singing saw.

The common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw's sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory, and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high-quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators and offers a robust principle to design high-quality resonators across scales, from macroscopic instruments to nanoscale devices, simply through geometry.

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets.

Recent advances in the manipulation of the orbital angular momentum (OAM) within the paradigm of orbitronics presents a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi2Te4 as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work, we open up new possibilities for innovative applications in topological spintronics and orbitronics.

Magneto-optical Effects of an Artificially Layered Ferromagnetic Topological Insulator with a TC of 160 K.

Magnetic topological insulators are a fertile platform for studying the interplay between magnetism and topology. The unique electronic band structure can induce exotic transport and optical properties. However, a comprehensive optical study at both near-infrared and terahertz frequencies has been lacking. Here, we report magneto-optical effects from a heterostructure of a Cr-incorporated topological insulator, CBST. By measuring the magneto-optical Kerr effect, we observe a high temperature ferromagnetic transition (160 K) in the CBST film. We also use time-domain terahertz polarimetry to reveal a terahertz Faraday rotation of 1.5 mrad and a terahertz Kerr rotation of 3.6 mrad at 2 K. The calculated terahertz Hall conductance is 0.42 e2/h. Our work shows the optical responses of an artificially layered magnetic topological insulator, paving the way toward a high-temperature quantum anomalous Hall effect via heterostructure engineering.

Design of Antiferromagnetic Second-Order Band Topology with Rotation Topological Invariants in Two Dimensions.

The existence of fractionally quantized topological corner charge serves as a key indicator for two-dimensional (2D) second-order topological insulators (SOTIs), yet it has not been experimentally observed in realistic materials. Here, based on effective model analysis and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in 2D systems with antiferromagnetic (AFM) order. We discover that the band topology originates from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Using first-principles calculations, we show that the 2D AFM SOTI phase can be realized in (MnBi2Te4)(Bi2Te3)m films. Moreover, we demonstrate that the SOTI states are linked to rotation topological invariants under 3-fold rotation symmetry C3, resulting in fractionally quantized corner charge, i.e., n3|e| (mod e). Due to the great achievements in (MnBi2Te4)(Bi2Te3)m systems, our results providing reliable material candidates for experimentally accessible AFM SOTIs should draw intense attention.

Unveiling correlated two-dimensional topological insulators through fermionic tensor network states-classification, edge theories and variational wavefunctions.

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of electronic bands becomes obsolete, it has been established that topological insulator phases persist as stable phases, separate from the trivial insulators. However, due to the inability to express the ground states of such systems as Slater determinants, the formulation of generic variational wave functions for numerical simulations is highly desirable. In this paper, we tackle this challenge for two-dimensional topological insulators by developing a comprehensive framework for fermionic tensor network states. Starting from simple assumptions, we obtain possible sets of tensor equations for any given symmetry group, capturing consistent relations governing symmetry transformation rules on tensor legs. We then examine the connection between these tensor equations andnon-chiraltopological insulators by constructing edge theories and extracting quantum anomaly data from each set of tensor equations. By exhaustively exploring all possible sets of equations, we achieve a systematic classification of non-chiral topological insulator phases. Imposing the solutions of a given set of equations onto local tensors, we obtain generic variational wavefunctions for the corresponding topological insulator phases. Our methodology provides an important step toward simulating topological insulators in strongly correlated systems. We discuss the limitations and potential generalizations of our results, paving the way for further advancements in this field.

Holographic Nano-Imaging of Terahertz Dirac Plasmon Polaritons in Topological Insulator Antenna Resonators.

Excitation of Dirac plasmon polaritons (DPPs) in bi-dimensional materials have attracted considerable interest in recent years, both from perspectives of understanding their physics and exploring their transformative potential for nanophotonic devices, including ultra-sensitive plasmonic sensors, ultrafast saturable absorbers, modulators, and switches. Topological insulators (TIs) represent an ideal technological platform in this respect because they can support plasmon polaritons formed by Dirac carriers in the topological surface states. Tracing propagation of DPPs is a very challenging task, particularly at terahertz (THz) frequencies, where the DPP wavelength becomes over one order of magnitude shorter than the free space photon wavelength. Furthermore, severe attenuation hinders the comprehensive analysis of their characteristics. Here, the properties of DPPs in real TI-based devices are revealed. Bi2Se3 rectangular antennas can efficiently confine the propagation of DPPs to a single dimension and, as a result, enhance the DPPs visibility despite the strong intrinsic attenuation. The plasmon dispersion and loss properties from plasmon profiles are experimentally determined, along the antennas, obtained using holographic near-field nano-imaging in a wide range of THz frequencies, from 2.05 to 4.3 THz. The detailed investigation of the unveiled DPP properties can guide the design of novel topological quantum devices exploiting their directional propagation.

Giant and Tunable Out-of-Plane Spin Polarization of Topological Antimonene.

Topological insulators are bulk insulators with metallic and fully spin-polarized surface states displaying Dirac-like band dispersion. Due to spin-momentum locking, these topological surface states (TSSs) have a predominant in-plane spin polarization in the bulk fundamental gap. Here, we show by spin-resolved photoemission spectroscopy that the TSS of a topological insulator interfaced with an antimonene bilayer exhibits nearly full out-of-plane spin polarization within the substrate gap. We connect this phenomenon to a symmetry-protected band crossing of the spin-polarized surface states. The nearly full out-of-plane spin polarization of the TSS occurs along a continuous path in the energy-momentum space, and the spin polarization within the gap can be reversibly tuned from nearly full out-of-plane to nearly full in-plane by electron doping. These findings pave the way to advanced spintronics applications that exploit the giant out-of-plane spin polarization of TSSs.

Universal Conductance Fluctuations in a MnBi2Te4 Thin Film.

Quantum coherence of electrons can produce striking behaviors in mesoscopic conductors. Although magnetic order can also strongly affect transport, the combination of coherence and magnetic order has been largely unexplored. Here, we examine quantum coherence-driven universal conductance fluctuations in the antiferromagnetic, canted antiferromagnetic, and ferromagnetic phases of a thin film of the topological material MnBi2Te4. In each magnetic phase, we extract a charge carrier phase coherence length of about 100 nm. The conductance magnetofingerprint is repeatable when sweeping applied magnetic field within one magnetic phase. Surprisingly, in the antiferromagnetic and canted antiferromagnetic phases, but not in the ferromagnetic phase, the magnetofingerprint depends on the direction of the field sweep. To explain our observations, we suggest that conductance fluctuation measurements are sensitive to the motion and nucleation of magnetic domain walls in MnBi2Te4.

Robust Second-Order Topological Insulators with Giant Valley Polarization in Two-Dimensional Honeycomb Ferromagnets.

Magnetic topological states have attracted great attention that provide exciting platforms for exploring prominent physical phenomena and applications of topological spintronics. Here, using a tight-binding model and first-principles calculations, we put forward that, in contrast to previously reported magnetic second-order topological insulators (SOTIs), robust SOTIs can emerge in two-dimensional ferromagnets regardless of magnetization directions. Remarkably, we identify intrinsic ferromagnetic 2H-RuCl2 and Janus VSSe monolayers as experimentally feasible candidates of predicted robust SOTIs with the emergence of nontrivial corner states along different magnetization directions. Moreover, under out-of-plane magnetization, we unexpectedly point out that the valley polarization of SOTIs can be huge and much larger than that of the known ferrovalley materials, opening up a technological avenue to bridge the valleytronics and higher-order topology with high possibility of innovative applications in topological spintronics and valleytronics.

Large Exchange Bias Effect and Coverage-Dependent Interfacial Coupling in CrI3/MnBi2Te4 van der Waals Heterostructures.

Igniting interface magnetic ordering of magnetic topological insulators by building a van der Waals heterostructure can help to reveal novel quantum states and design functional devices. Here, we observe an interesting exchange bias effect, indicating successful interfacial magnetic coupling, in CrI3/MnBi2Te4 ferromagnetic insulator/antiferromagnetic topological insulator (FMI/AFM-TI) heterostructure devices. The devices originally exhibit a negative exchange bias field, which decays with increasing temperature and is unaffected by the back-gate voltage. When we change the device configuration to be half-covered by CrI3, the exchange bias becomes positive with a very large exchange bias field exceeding 300 mT. Such sensitive manipulation is explained by the competition between the FM and AFM coupling at the interface of CrI3 and MnBi2Te4, pointing to coverage-dependent interfacial magnetic interactions. Our work will facilitate the development of topological and antiferromagnetic devices.

Observation of Gapped Topological Surface States and Isolated Surface Resonances in PdTe2 Ultrathin Films.

The superconductor PdTe2 is known to host bulk Dirac bands and topological surface states. The coexistence of superconductivity and topological surface states makes PdTe2 a promising platform for exploring topological superconductivity and Majorana bound states. In this work, we report the spectroscopic characterization of ultrathin PdTe2 films with thickness down to three monolayers (ML). In the 3 ML PdTe2 film, we observed spin-polarized surface resonance states, which are isolated from the bulk bands due to the quantum size effects. In addition, the hybridization of surface states on opposite faces leads to a thickness-dependent gap in the topological surface Dirac bands. Our photoemission results show clearly that the size of the hybridization gap increases as the film thickness is reduced. The observation of isolated surface resonances and gapped topological surface states sheds light on the applications of PdTe2 quantum films in spintronics and topological quantum computation.

Nondegenerate Integer Quantum Hall Effect from Topological Surface States in Ag2Te Nanoplates.

The quantum Hall effect is one of the exclusive properties displayed by Dirac Fermions in topological insulators, which propagates along the chiral edge state and gives rise to quantized electron transport. However, the quantum Hall effect formed by the nondegenerate Dirac surface states has been elusive so far. Here, we demonstrate the nondegenerate integer quantum Hall effect from the topological surface states in three-dimensional (3D) topological insulator ß-Ag2Te nanostructures. Surface-state dominant conductance renders quantum Hall conductance plateaus with a step of e2/h, along with typical thermopower behaviors of two-dimensional (2D) massless Dirac electrons. The 2D nature of the topological surface states is proven by the electrical and thermal transport responses under tilted magnetic fields. Moreover, the degeneracy of the surface states is removed by structure inversion asymmetry (SIA). The evidenced SIA-induced nondegenerate integer quantum Hall effect in low-symmetry ß-Ag2Te has implications for both fundamental study and the realization of topological magneto-electric effects.

Current-Phase Relation of a WTe2 Josephson Junction.

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe2. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTex inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 µm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Aharonov-Bohm Interference and Phase-Coherent Surface-State Transport in Topological Insulator Rings.

We present low-temperature magnetotransport measurements on selectively grown Sb2Te3-based topological insulator ring structures. These devices display clear Aharonov-Bohm oscillations in the conductance originating from phase-coherent transport around the ring. The temperature dependence of the oscillation amplitude indicates that the Aharonov-Bohm oscillations originate from ballistic transport along the ring arms. We attribute these oscillations to the topological surface states. Further insight into the phase coherence is gained by comparing with similar Aharonov-Bohm-type oscillations in topological insulator nanoribbons exposed to an axial magnetic field. Here, quasi-ballistic phase-coherent transport is confirmed for closed-loop topological surface states in the transverse direction enclosing the nanoribbon. In contrast, the appearance of universal conductance fluctuations indicates phase-coherent transport in the diffusive regime, which is attributed to bulk carrier transport. Thus, it appears that even in the presence of diffusive p-type charge carriers in Aharonov-Bohm ring structures, phase-coherent quasi-ballistic transport of topological surface states is maintained over long distances.

Van der Waals Engineering of Ultrafast Carrier Dynamics in Magnetic Heterostructures.

Heterostructures composed of the intrinsic magnetic topological insulator MnBi2Te4 and its nonmagnetic counterpart Bi2Te3 host distinct surface electronic band structures depending on the stacking order and exposed termination. Here, we probe the ultrafast dynamical response of MnBi2Te4 and MnBi4Te7 following near-infrared optical excitation using time- and angle-resolved photoemission spectroscopy and disentangle surface from bulk dynamics based on density functional theory slab calculations of the surface-projected electronic structure. We gain access to the out-of-equilibrium charge carrier populations of both MnBi2Te4 and Bi2Te3 surface terminations of MnBi4Te7, revealing an instantaneous occupation of states associated with the Bi2Te3 surface layer followed by carrier extraction into the adjacent MnBi2Te4 layers with a laser fluence-tunable delay of up to 350 fs. The ensuing thermal relaxation processes are driven by phonon scattering with significantly slower relaxation times in the magnetic MnBi2Te4 septuple layers. The observed competition between interlayer charge transfer and intralayer phonon scattering demonstrates a method to control ultrafast charge transfer processes in MnBi2Te4-based van der Waals compounds.

Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants.

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle-resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi2Se2Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect.

Topological Insulator Bi2 Se3 -Assisted Heterostructure for Ultrafast Charging Sodium-Ion Batteries.

The development of fast charging materials offers a viable solution for large-scale and sustainable energy storage needs. However, it remains a critical challenge to improve the electrical and ionic conductivity for better performance. Topological insulator (TI), a topological quantum material that has attracted worldwide attention, hosts unusual metallic surface states and consequent high carrier mobility. Nevertheless, its potential in promising high-rate charging capability has not been fully realized and explored. Herein, a novel Bi2 Se3 -ZnSe heterostructure as excellent fast charging material for Na+ storage is reported. Ultrathin Bi2 Se3 nanoplates with rich TI metallic surfaces are introduced as an electronic platform inside the material, which greatly reduces the charge transfer resistance and improves the overall electrical conductivity. Meanwhile, the abundant crystalline interfaces between these two selenides promote Na+ migration and provide additional active sites as well. As expected, the composite delivers the excellent high-rate performance of 360.5 mAh g-1 at 20 A g-1 and maintains its electrochemical stability of 318.4 mAh g-1 after 3000 long cycles, which is the record high for all reported selenide-based anodes. This work is anticipated to provide alternative strategies for further exploration of topological insulators and advanced heterostructures.

Utilizing Topological Insulator Two-Dimensional Bismuth for Ultrasensitive Acoustic Detection.

Topological insulators (TIs) are characterized by a full insulating gap in the bulk and gapless edge or surface states, which have attracted tremendous attention. 2D Bi (110), as a typical TI, is of particular interest due to its low symmetry structure and topologically protected and spin-momentum-locked Dirac surface states. However, the material's potential applications are hindered by difficulties in fabrication, due to its strong semi-metallic bonding and poor stability. In this study, a novel electrochemical intercalation method for the fabrication of ultrathin Bi (110) nanosheets with the highest yield ever reported is presented. These nanosheets are stabilized through cathodic exfoliation in a reductive environment and further modification with polymer ionic liquids. The versatility of these nanosheets is demonstrated by fabricating flexible acoustic sensors with ultrahigh sensitivity. These sensors can even detect sounds as quiet as 45 dB. Furthermore, these sensors are utilized for acoustic-to-electric energy conversion and information transfer. This work offers a promising approach for scalable fabrication and preservation of ultrathin 2D TI Bi (110) nanosheets and paves the way for their integration into smart devices.

Engineering Second-Order Corner States in 2D Multiferroics.

The understanding and manipulate of the second-order corner states are central to both fundamental physics and future topotronics applications. Despite the fact that numerous second-order topological insulators (SOTIs) are achieved, the efficient engineering in a given material remains elusive. Here, the emergence of 2D multiferroics SOTIs in SbAs and BP5 monolayers is theoretically demonstrated, and an efficient and straightforward way for engineering the nontrivial corner states by ferroelasticity and ferroelectricity is remarkably proposed. With ferroelectric polarization of SbAs and BP5 monolayers, the nontrivial corner states emerge in the mirror symmetric corners and are perpendicular to orientations of the in-plane spontaneous polarization. And remarkably the spatial distribution of the corner states can be effectively tuned by a ferroelastic switching. At the intermediate states of both ferroelectric and ferroelastic switchings, the corner states disappear. These finding not only combines exotic SOTIs with multiferroics but also pave the way for experimental discovery of 2D tunable SOTIs.

Density-Dependence of Surface Transport in Tellurium-Enriched Nanograined Bulk Bi2 Te3.

Three-dimensional topological insulators (3D TI) exhibit conventional parabolic bulk bands and protected Dirac surface states. A thorough investigation of the different transport channels provided by the bulk and surface carriers using macroscopic samples may provide a path toward accessing superior surface transport properties. Bi2 Te3 materials make promising 3D TI models; however, due to their complicated defect chemistry, these materials have a high number of charge carriers in the bulk that dominate the transport, even as nanograined structures. To partially control the bulk charge carrier density, herein the synthesis of Te-enriched Bi2 Te3 nanoparticles is reported. The resulting nanoparticles are compacted into nanograined pellets of varying porosity to tailor the surface-to-volume ratio, thereby emphasizing the surface transport channels. The nanograined pellets are characterized by a combination of resistivity, Hall- and magneto-conductance measurements together with (THz) time-domain reflectivity measurements. Using the Hikami-Larkin-Nagaoka (HLN) model, a characteristic coherence length of ≈200 nm is reported that is considerably larger than the diameter of the nanograins. The different contributions from the bulk and surface carriers are disentangled by THz spectroscopy, thus emphasizing the dominant role of the surface carriers. The results strongly suggest that the surface transport carriers have overcome the hindrance imposed by nanoparticle boundaries.