Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe_{3}Sn_{2}

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe_{3}Sn_{2} displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects.

Symmetry-selective quasiparticle scattering and electric field tunability of the ZrSiS surface electronic structure

Three-dimensional Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X = Si, Ge; Y = S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role in such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering reported between states of different symmetry eigenvalues at small wave vectorq⃗.Here we show, using quasiparticle interference, that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g. native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state, can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin-orbit induced avoided crossing near the Fermi level by as much as 300%.

Interfacial magnetic spin Hall effect in van der Waals Fe3GeTe2/MoTe2 heterostructure

The spin Hall effect (SHE) allows efficient generation of spin polarization or spin current through charge current and plays a crucial role in the development of spintronics. While SHE typically occurs in non-magnetic materials and is time-reversal even, exploring time-reversal-odd (T-odd) SHE, which couples SHE to magnetization in ferromagnetic materials, offers a new charge-spin conversion mechanism with new functionalities. Here, we report the observation of giant T-odd SHE in Fe3GeTe2/MoTe2 van der Waals heterostructure, representing a previously unidentified interfacial magnetic spin Hall effect (interfacial-MSHE). Through rigorous symmetry analysis and theoretical calculations, we attribute the interfacial-MSHE to a symmetry-breaking induced spin current dipole at the vdW interface. Furthermore, we show that this linear effect can be used for implementing multiply-accumulate operations and binary convolutional neural networks with cascaded multi-terminal devices. Our findings uncover an interfacial T-odd charge-spin conversion mechanism with promising potential for energy-efficient in-memory computing.

Heavy-to-light electron transition enabling real-time spectra detection of charged particles by a biocompatible semiconductor

The current challenge of wearable/implantable personal dosimeters for medical diagnosis and radiotherapy applications is lack of suitable detector materials possessing both excellent detection performance and biocompatibility. Here, we report a solution-grown biocompatible organic single crystalline semiconductor (OSCS), 4-Hydroxyphenylacetic acid (4HPA), achieving real-time spectral detection of charged particles with single-particle sensitivity. Along in-plane direction, two-dimensional anisotropic 4HPA exhibits a large electron drift velocity of 5 × 105 cm s-1 at "radiation-mode" while maintaining a high resistivity of (1.28 ± 0.003) × 1012 Ω·cm at "dark-mode" due to influence of dense π-π overlaps and high-energy L1 level. Therefore, 4HPA detectors exhibit the record spectra detection of charged particles among their organic counterparts, with energy resolution of 36%, (μt)e of (4.91 ± 0.07) × 10-5 cm2 V-1, and detection time down to 3 ms. These detectors also show high X-ray detection sensitivity of 16,612 μC Gyabs-1 cm-3, detection of limit of 20 nGyair s-1, and long-term stability after 690 Gyair irradiation.

Orbital Origin of the Intrinsic Planar Hall Effect

Recent experiments reported an antisymmetric planar Hall effect, where the Hall current is odd in the in plane magnetic field and scales linearly with both electric and magnetic fields applied. Existing theories rely exclusively on a spin origin, which requires spin-orbit coupling to take effect. Here, we develop a general theory for the intrinsic planar Hall effect (IPHE), highlighting a previously unknown orbital mechanism and connecting it to a band geometric quantity-the anomalous orbital polarizability (AOP). Importantly, the orbital mechanism does not request spin-orbit coupling, so sizable IPHE can occur and is dominated by an orbital contribution in systems with weak spin-orbit coupling. Combined with first-principles calculations, we demonstrate our theory with quantitative evaluation for bulk materials TaSb_{2}, NbAs_{2}, and SrAs_{3}. We further show that AOP and its associated orbital IPHE can be greatly enhanced at topological band crossings, offering a new way to probe topological materials.

The Coexistence of Superconductivity and Topological Order in Van der Waals InNbS2

The research on systems with coexistence of superconductivity and nontrivial band topology has attracted widespread attention. However, the limited availability of material platforms severely hinders the research progress. Here, it reports the first experimental synthesis and measurement of high-quality single crystal van der Waals transition-metal dichalcogenide InNbS2 , revealing it as a topological nodal line semimetal with coexisting superconductivity. The temperature-dependent measurements of magnetization susceptibility and electrical transport show that InNbS2 is a type-II superconductor with a transition temperature Tc of 6 K. First-principles calculations predict multiple topological nodal ring states close to the Fermi level in the presence of spin-orbit coupling. Similar features are also observed in the as-synthesized BiNbS2 and PbNbS2 samples. This work provides new material platforms ANbS2 (A = In, Bi, and Pb) and uncovers their intriguing potential for exploring the interplay between superconductivity and band topology.

Giant and Nonanalytic Negative Piezoelectric Response in Elemental Group-Va Ferroelectric Monolayers

Materials with negative longitudinal piezoelectric response have been a focus of recent research. So far, reported examples are mostly three-dimensional bulk materials, either compounds with strong ionic bonds or layered materials with van der Waals interlayer gaps. Here, we report the first example in two-dimensional elemental materials-the class of group-Va monolayers. From first-principles calculations, we show that these materials possess giant negative longitudinal piezoelectric coefficient e_{11}. Importantly, its physical mechanism is also distinct from all previous proposals, connected with the special buckling driven polarization in these elemental systems. As a result, the usually positive internal strain contribution to piezoelectricity becomes negative and even dominates over the clamped ion contribution in Bi monolayers. Based on this new mechanism, we also find several 2D crystal structures that may support negative longitudinal piezoelectricity. As another consequence, piezoelectric response in Bi monolayers exhibits a significant nonanalytic behavior, namely, the e_{11} coefficient takes sizably different values (differed by ∼18%) under tensile and compressive strains, a phenomenon not known before and helpful for the development of novel electromechanical devices.

Magnetic Real Chern Insulator in 2D Metal-Organic Frameworks

Real Chern insulators have attracted great interest, but so far, their material realization is limited to nonmagnetic crystals and systems without spin-orbit coupling. Here, we reveal the magnetic real Chern insulator (MRCI) state in a recently synthesized metal-organic framework material Co3(HITP)2. Its ground state with in-plane ferromagnetic ordering hosts a nontrivial real Chern number, enabled by the C2zT symmetry and robustness against spin-orbit coupling. Distinct from previous nonmagnetic examples, the topological corner zero modes of MRCIs are spin-polarized. Furthermore, under small tensile strains, the material undergoes a topological phase transition from the MRCI to a magnetic double-Weyl semimetal phase, via a pseudospin-1 critical state. Similar physics can also be found in closely related materials Mn3(HITP)2 and Fe3(HITP)2, which also exist. Possible experimental detections and implications of an emerging magnetic flat band in the system are discussed.

Two-dimensional ferroelectricity in a single-element bismuth monolayer

Ferroelectric materials are fascinating for their non-volatile switchable electric polarizations induced by the spontaneous inversion-symmetry breaking. However, in all of the conventional ferroelectric compounds, at least two constituent ions are required to support the polarization switching1,2. Here, we report the observation of a single-element ferroelectric state in a black phosphorus-like bismuth layer3, in which the ordered charge transfer and the regular atom distortion between sublattices happen simultaneously. Instead of a homogenous orbital configuration that ordinarily occurs in elementary substances, we found the Bi atoms in a black phosphorous-like Bi monolayer maintain a weak and anisotropic sp orbital hybridization, giving rise to the inversion-symmetry-broken buckled structure accompanied with charge redistribution in the unit cell. As a result, the in-plane electric polarization emerges in the Bi monolayer. Using the in-plane electric field produced by scanning probe microscopy, ferroelectric switching is further visualized experimentally. Owing to the conjugative locking between the charge transfer and atom displacement, we also observe the anomalous electric potential profile at the 180° tail-to-tail domain wall induced by competition between the electronic structure and electric polarization. This emergent single-element ferroelectricity broadens the mechanism of ferroelectrics and may enrich the applications of ferroelectronics in the future.

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe_{2}, and in ferromagnetic monolayer MnSe_{2}, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.

Intrinsic Nonlinear Planar Hall Effect

We propose an intrinsic nonlinear planar Hall effect, which is of band geometric origin, independent of scattering, and scales with the second order of electric field and first order of magnetic field. We show that this effect is less symmetry constrained compared with other nonlinear transport effects and is supported in a large class of nonmagnetic polar and chiral crystals. Its characteristic angular dependence provides an effective way to control the nonlinear output. Combined with first-principles calculations, we evaluate this effect in the Janus monolayer MoSSe and report experimentally measurable results. Our work reveals an intrinsic transport effect, which offers a new tool for material characterization and a new mechanism for nonlinear device application.

Universal Molecular Control Strategy for Scalable Fabrication of Perovskite Light-Emitting Diodes

Despite the rapid progress in perovskite light-emitting diodes (PeLEDs), the electroluminescence performance of large-area perovskite devices lags far behind that of laboratory-size ones. Here, we report a 3.5 cm × 3.5 cm large-area PeLED with a record-high external quantum efficiency of 12.1% by creating an amphipathic molecular interface modifier of betaine citrate (BC) between the perovskite layer and the underlying hole transport layer (HTL). It is found that the surface wettability for various HTLs can be efficiently improved as a result of the coexistence of methyl and carboxyl groups in the BC molecules that makes favorable groups to selectively contact with the HTL surface and increases the surface free energy, which greatly facilitates the scalable process of solution-processed perovskite films. Moreover, the luminous performance of perovskite emitters is simultaneously enhanced through the coordination between C═O in the carboxyl groups and Pb dangling bonds.

Two-dimensional Janus Si dichalcogenides: a first-principles study

Strong structural asymmetry is actively explored in two-dimensional (2D) materials, because it can give rise to many interesting physical properties. Motivated by the recent synthesis of monolayer Si₂Te₂, we explored a family of 2D materials, named Janus Si dichalcogenides (JSD), which parallel the Janus transition metal dichalcogenides and exhibit even stronger inversion asymmetry. Using first-principles calculations, we show that their strong structural asymmetry leads to a pronounced intrinsic polar field, sizable spin splitting, and large piezoelectric response. The spin splitting involves an out-of-plane spin component, which is beyond the linear Rashba model. The piezoelectric tensor has a large value in both in-plane d₁₁ coefficient and out-of-plane d₃₁ coefficient, making monolayer JSDs distinct among existing 2D piezoelectric materials. In addition, we find interesting strain-induced phase transitions in these materials. Particularly, there are multiple valleys that compete for the conduction band minimum, which will lead to notable changes in the optical and transport properties under strain. Our work reveals a new family of Si based 2D materials, which could find promising applications in spintronic and piezoelectric devices.

Control over Berry Curvature Dipole with Electric Field in WTe_{2}

Berry curvature dipole plays an important role in various nonlinear quantum phenomena. However, the maximum symmetry allowed for nonzero Berry curvature dipole in the transport plane is a single mirror line, which strongly limits its effects in materials. Here, via probing the nonlinear Hall effect, we demonstrate the generation of Berry curvature dipole by applied dc electric field in WTe_{2}, which is used to break the symmetry constraint. A linear dependence between the dipole moment of Berry curvature and the dc electric field is observed. The polarization direction of the Berry curvature is controlled by the relative orientation of the electric field and crystal axis, which can be further reversed by changing the polarity of the dc field. Our Letter provides a route to generate and control Berry curvature dipole in broad material systems and to facilitate the development of nonlinear quantum devices.

Discovery of a maximally charged Weyl point

The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantised chiral charges, which can be measured by counting the number of Fermi arcs emanating from the corresponding Weyl points. It is known that merging unit-charged Weyl particles can create new ones with more charges. However, only very recently has it been realised that there is an upper limit - the maximal charge number that a two-fold Weyl point can host is four - achievable only in crystals without spin-orbit coupling. Here, we report the experimental realisation of such a maximally charged Weyl point in a three-dimensional photonic crystal. The four charges support quadruple-helicoid Fermi arcs, forming an unprecedented topology of two non-contractible loops in the surface Brillouin zone. The helicoid Fermi arcs also exhibit the long-pursued type-II van Hove singularities that can reside at arbitrary momenta. This discovery reveals a type of maximally charged Weyl particles beyond conventional topological particles in crystals.

Topological Chern vectors in three-dimensional photonic crystals

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator^1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector^6,7, similar to the three-dimensional (3D) quantum Hall effect^8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.

Intrinsic Nonlinear Electric Spin Generation in Centrosymmetric Magnets

We propose an intrinsic nonlinear electric spin generation effect, which can dominate in centrosymmetric magnets. We reveal the band geometric origin of this effect and clarify its symmetry characters. As an intrinsic effect, it is determined solely by the material's band structure and represents a material characteristic. Combining our theory with first-principle calculations, we predict sizable nonlinear spin generation in single-layer MnBi_{2}Te_{4}, which can be detected in experiment. Our theory opens a new route for all-electric controlled spintronics in centrosymmetric magnets which reside outside of the current paradigm based on linear spin response.

Realization of unpinned two-dimensional dirac states in antimony atomic layers

Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\Gamma }}}$$\end{document}Γ¯ in topological insulators Bi₂Se(Te)₃ and Dirac cones at K and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^{\prime}$$\end{document}K′ points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene.

In graphene and on the surfaces of many topological insulators, the Dirac cones are pinned to high symmetry points in reciprocal space. Here, the authors report that the Dirac cones in atomically-thin Sb layers occur at generic reciprocal-space points which can be tuned by lattice strain.

2D Multiferroicity with Ferroelectric Switching Induced Spin-Constrained Photoelectricity

Multiferroic materials with tunable magnetoelectric orders enable the integration of sensing, data storage, and processing into one single device. The scarcity of single-phase multiferroics spurs extensive research in pursuit of composite systems combining different types of ferroic materials. In this work, spin-constrained photoelectric memory is proposed in two-dimensional (2D) layered magnetic/ferroelectric heterostructures, holding the possibility of low-power electrical write operation and nondestructive optical read operation. The ground state of ferromagnetic (FM) and antiferromagnetic (AFM) orderings in the magnetic layer is altered by polarization direction of the ferroelectric layer. Specifically, the FM heterostructure exhibits a type-II band alignment. Due to the light-induced charge transfer, spin-polarized/unpolarized current arises from the FM/AFM state, which can be recorded as the "1"/"0" state and served for logic processing and memory applications. Our first-principles calculations demonstrate that the NiI₂/In₂Se₃ heterobilayer is an ideal candidate to realize such a spin-dependent photoelectric memory. The reversible FM state (easy-axis magnetic anisotropy) and AFM state (easy-plane magnetic orientation) in the NiI₂ layer originate from interfacial charge transfer and effective electric field due to the proximity effect. This work offers considerable potential in the integration of memory processing capability into one single device with 2D layered multiferroic heterostructures.

Large Magnetic Gap in a Designer Ferromagnet-Topological Insulator-Ferromagnet Heterostructure

Combining magnetism and nontrivial band topology gives rise to quantum anomalous Hall (QAH) insulators and exotic quantum phases such as the QAH effect where current flows without dissipation along quantized edge states. Inducing magnetic order in topological insulators via proximity to a magnetic material offers a promising pathway toward achieving the QAH effect at a high temperature for lossless transport applications. One promising architecture involves a sandwich structure comprising two single-septuple layers (1SL) of MnBi₂ Te₄ (a 2D ferromagnetic insulator) with ultrathin few quintuple layer (QL) Bi₂ Te₃ in the middle, and it is predicted to yield a robust QAH insulator phase with a large bandgap greater than 50 meV. Here, the growth of a 1SL MnBi₂ Te₄ /4QL Bi₂ Te₃ /1SL MnBi₂ Te₄ heterostructure via molecular beam epitaxy is demonstrated and the electronic structure probed using angle-resolved photoelectron spectroscopy. Strong hexagonally warped massive Dirac fermions and a bandgap of 75 ± 15 meV are observed. The magnetic origin of the gap is confirmed by the observation of the exchange-Rashba effect, as well as the vanishing bandgap above the Curie temperature, in agreement with density functional theory calculations. These findings provide insights into magnetic proximity effects in topological insulators and reveal a promising platform for realizing the QAH effect at elevated temperatures.

Topological band transition between hexagonal and triangular lattices with (px,py) orbitals

By combining tight-binding modelling with density functional theory based first-principles calculations, we investigate the band evolution of two-dimensional (2D) hexagonal lattices with (p_x,p_y) orbitals, focusing on the electronic structures and topological phase transitions. The (p_x,p_y)-orbital hexagonal lattice model possesses two flat bands encompassing two linearly dispersive Dirac bands. Breaking the A/B sublattice symmetry could transform the model into two triangular lattices, each featuring a flat band and a dispersive band. Inclusion of the spin-orbit coupling and magnetization may give rise to quantum spin Hall and quantum anomalous Hall (QAH) states. As a proof of concept, we demonstrate that half-hydrogenated stanene is encoded by a triangular lattice with (p_x,p_y) orbitals, which exhibits ferromagnetism and QAH effect with a topological gap of ∼0.15 eV, feasible for experimental observation. These results provide insights into the structure-property relationships involving the orbital degree of freedom, which may shed light on future design and preparation of 2D topological materials for novel electronic/spintronic and quantum computing devices.

Projectively Enriched Symmetry and Topology in Acoustic Crystals

Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z_{2} gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.

Designing Ultra-flat Bands in Twisted Bilayer Materials at Large Twist Angles: Theory and Application to Two-Dimensional Indium Selenide

Intertwisted bilayers of two-dimensional (2D) materials can host low-energy flat bands, which offer opportunity to investigate many intriguing physics associated with strong electron correlations. In the existing systems, ultra-flat bands only emerge at very small twist angles less than a few degrees, which poses a challenge for experimental studies and practical applications. Here, we propose a new design principle to achieve low-energy ultra-flat bands with increased twist angles. The key condition is to have a 2D semiconducting material with a large energy difference of band edges controlled by stacking. We show that the interlayer interaction leads to defect-like states under twisting, which forms a flat band in the semiconducting band gap with dispersion strongly suppressed by the large energy barriers in the moiré superlattice even for large twist angles. We explicitly demonstrate our idea in bilayer α-In₂Se₃ and bilayer InSe. For bilayer α-In₂Se₃, we show that a twist angle of ∼13.2° is sufficient to achieve the band flatness comparable to that of twist bilayer graphene at the magic angle ∼1.1°. In addition, the appearance of ultra-flat bands here is not sensitive to the twist angle as in bilayer graphene, and it can be further controlled by external gate fields. Our finding provides a new route to achieve ultra-flat bands other than reducing the twist angles and paves the way toward engineering such flat bands in a large family of 2D materials.

Chiral Phonon Diode Effect in Chiral Crystals

The diode effect means that carriers can only flow in one direction but not the other. While diode effects for electron charge, spin, or photon have been widely discussed, it remains a question whether a chiral phonon diode can be realized, which utilizes the chiral degree of freedom of lattice vibrations. In this work, we reveal an intrinsic connection between the chiralities of a crystal structure and its phonon excitations, which naturally leads to the chiral phonon diode effect in chiral crystals. At a certain frequency, phonons with a definite chirality can propagate only in one direction but not the opposite. We demonstrate the idea in concrete materials including bulk Te and α-quartz (SiO₂). Our work discovers the fundamental physics of chirality coupling between different levels of a system, and the predicted effect will provide a new route to control phonon transport and design information devices.

Room-temperature third-order nonlinear Hall effect in Weyl semimetal TaIrTe4

The second-order nonlinear Hall effect observed in the time-reversal symmetric system has not only shown abundant physical content, but also exhibited potential application prospects. Recently, a third-order nonlinear Hall effect has been observed in MoTe₂ and WTe₂. However, few-layer MoTe₂ and WTe₂ are usually unstable in air and the observed third-order nonlinear Hall effect can be measured only at low temperature, which hinders further investigation as well as potential application. Thus, exploring new air-stable material systems with a sizable third-order nonlinear Hall effect at room temperature is an urgent task. Here, in type-II Weyl semimetal TaIrTe₄, we observed a pronounced third-order nonlinear Hall effect, which can exist at room temperature and remain stable for months. The third-order nonlinear Hall effect is connected to the Berry-connection polarizability tensor instead of the Berry curvature. The possible mechanism of the observation of the third-order nonlinear Hall effect in TaIrTe₄ at room temperature has been discussed. Our findings will open an avenue towards exploring room-temperature nonlinear devices in new quantum materials.

Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne

Real topological phases featuring real Chern numbers and second-order boundary modes have been a focus of current research, but finding their material realization remains a challenge. Here, based on first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized three-dimensional (3D) graphdiyne as the first realistic example of the recently proposed second-order real nodal-line semimetal. We show that the material hosts a pair of real nodal rings, each protected by two topological charges: a real Chern number and a 1D winding number. The two charges generate distinct topological boundary modes at distinct boundaries. The real Chern number leads to a pair of hinge Fermi arcs, whereas the winding number protects a double drumhead surface bands. We develop a low-energy model for 3D graphdiyne which captures the essential topological physics. Experimental aspects and possible topological transition to a 3D real Chern insulator phase are discussed.

Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets

Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property-the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with PT symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn_{2}Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the Néel vector orientation with a 2π periodicity, which offers a new route for electric detection of the magnetic order in PT-invariant antiferromagnets.

Gauge-Field Extended k·p Method and Novel Topological Phases

Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i) The little co-group must include the translations with nontrivial algebraic relations. (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.

Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor

Nonlinear responses in transport measurements are linked to material properties not accessible at linear order¹ because they follow distinct symmetry requirements^2-5. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry¹. Recent experiments on ultrathin WTe₂ demonstrated this connection between crystal structure and nonlinear response^6,7. The observed second-order nonlinear Hall effect can probe the Berry curvature dipole, a band geometric property, in non-magnetic materials, just like the anomalous Hall effect probes the Berry curvature in magnetic materials^8,9. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor¹⁰, gives rise to higher-order signals, but it has not been probed experimentally. Here, we report a third-order nonlinear Hall effect in thick T_d-MoTe₂ samples. The third-order signal is found to be the dominant response over both the linear- and second-order ones. Angle-resolved measurements reveal that this feature results from crystal symmetry constraints. Temperature-dependent measurement shows that the third-order Hall response agrees with the Berry-connection polarizability contribution evaluated by first-principles calculations. The third-order nonlinear Hall effect provides a valuable probe for intriguing material properties that are not accessible at lower orders and may be employed for high-order-response electronic devices.

Layer-engineered interlayer excitons

Photoluminescence (PL) from excitons serves as a powerful tool to characterize the optoelectronic property and band structure of semiconductors, especially for atomically thin two-dimensional transition metal dichalcogenide (TMD) materials. However, PL quenches quickly when the thickness of TMD materials increases from monolayer to a few layers, due to the change from direct to indirect band transition. Here, we show that PL can be recovered by engineering multilayer heterostructures, with the band transition reserved to be a direct type. We report emission from layer-engineered interlayer excitons from these multilayer heterostructures. Moreover, as desired for valleytronics devices, the lifetime, valley polarization, and valley lifetime of the generated interlayer excitons can all be substantially improved as compared with that in the monolayer-monolayer heterostructure. Our results pave the way for controlling the properties of interlayer excitons by layer engineering.

Colossal Anomalous Hall Effect in Ferromagnetic van der Waals CrTe2

van der Waals crystals exhibit excellent material performance when exfoliated to few-atomic-layer thickness. In contrast, the van der Waals thin films more than 10 nm thick are believed to show bulk properties, in which outstanding material performance is rarely found. Here we report the largest anomalous Hall conductivity observed so far in a 170 nm van der Waals ferromagnetic 1T-CrTe₂ flake, which reaches 67,000 Ω^-1 cm^-1. Such a colossal anomalous Hall conductivity in 1T-CrTe₂ is dominated by the extrinsic skew scattering process rather than the intrinsic Berry phase effect, as evidenced by the linear relation between the anomalous Hall conductivity and the longitudinal conductivity. Defying the dilemma of mutually exclusive large anomalous Hall angle and high electric conductivity for most ferromagnets, 1T-CrTe₂ achieves both in a thin film sample. Considering the shared physics of the anomalous Hall effect and the spin Hall effect, our finding offers a guideline for searching large spin Hall materials of high conductivity which may overcome the bottleneck of overheating in spintronics devices.

Atomically Thin Quantum Spin Hall Insulators

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.

Functional Group-induced p-Doping of MoS2 by Titanium(IV) Bis(ammonium lactato) Dihydroxide Physisorption

P-type doping is of critical importance for the realization of certain high-performance electrical and optoelectronic devices based on molybdenum disulfide (MoS₂ ). Charge transfer doping is a feasible strategy for tuning the conductance properties via facile treatment. In this work, the electrical properties of few-layer MoS₂ were modulated with titanium(IV) bis(ammonium lactato) dihydroxide molecules (denoted as TALH) via physisorption. The functional groups such as electronegative hydroxyl (-OH) and carboxylate groups (-COO) included in TALH molecules are expected to induce p-doping effect through surface charge transfer when being attached to MoS₂ . The p-doping is proved by X-ray photoelectron spectroscopy (XPS) with the downshift of Mo 3d and S 2p peaks. Control experiments and density functional theory calculations validate that the p-type doping mainly originated from the -OH group in TALH, which drew electrons from MoS₂ . These results suggest that functional group-mediated p-doping effect show a path to modulate the carrier transition in MoS_2, and enrich the molecule series for device modification.

Unlocking Rapid and Robust Sodium Storage Performance of Zinc-Based Sulfide via Indium Incorporation

Zinc sulfide (ZnS) exhibits promise in sodium-ion batteries (SIBs) because of its low operation voltage and high theoretical specific capacity. However, pristine ZnS is not adequate in realizing rapid and robust sodium storage owing to its low reversibility, poor structure stability, and sluggish kinetics. To date, most efforts focus on utilizing carbonaceous incorporation to improve its electrochemical performances. Nevertheless, it remains an arduous challenge for realizing superior rate capability while obtaining stable cycling. Herein, inspired by the crystal structure of hexagonal ZnIn₂S₄, which possesses an intrinsic layered feature with larger unit-cell volume versus that of ZnS, indium incorporation is thus deployed as an immediate remedy. In/ex situ investigations combined with density functional theory calculations are conducted to reveal the superior kinetics, high reversibility, and good structure stability of ZnIn₂S₄. Notably, the formed indium-based derivatives during cycling manifest a Na⁺ (de)intercalation process, thereby exciting a synergetic mechanism to stabilize electrochemical cycling. As a result, the electrochemical performances of Zn-based sulfide are significantly improved via the indium incorporation. Furthermore, a full cell based on the ZnIn₂S₄ anode with the superior electrochemical performance is developed. This work provides an effective tactic of heteroatom incorporation for optimizing structure as well as exciting a complementary reaction process toward developing superior anodes for high-performance alkali-ion batteries.

Switching Spinless and Spinful Topological Phases with Projective PT Symmetry

A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via Z_{2} projective representations. For PT symmetry, this occurs when P inverses the gauge transformation needed to recover the original Z_{2} gauge connections under P. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.

One-Dimensional Metal Embedded in Two-Dimensional Semiconductor in Nb2Six-1Te4

The ternary van der Waals material Nb₂Si_x-1Te₄ demonstrates many interesting properties as the content of Si is changed, ranging from metallic Nb₃SiTe₆ (x = 5/3) to narrow-gap semiconductor Nb₂SiTe₄ (x = 2) and with the emergence of one-dimensional Dirac fermion excitations in between. An in-depth understanding of their properties with different stoichiometry is important. Here we use scanning tunneling microscopy and spectroscopy to reveal that Nb₂Si_x-1Te₄ is a system with spontaneously developed and self-aligned one-dimensional metallic chains embedded in a two-dimensional semiconductor. Electron quasiparticles form one- and two-dimensional standing waves side by side. This special microscopic structure results in strong transport anisotropy. Along the chain direction the material behaves like a metal, while perpendicular to the chain direction, it behaves like a semiconductor. These findings provide an important basis for further investigation of this intriguing system.

Propagating Chiral Phonons in Three-Dimensional Materials

Chiral phonons were initially proposed and experimentally verified in two-dimensional (2D) systems. Their intriguing effects have generated profound impacts on multiple research fields. However, all chiral phonons reported to date are constrained to be local, in the sense that their group velocities vanish identically. Here, we propose the concept of propagating 3D chiral phonons, which can transport the information on chirality and angular momentum. Guided by the necessary conditions and using first-principles calculations, we demonstrate their existence in WN₂. The chirality, group velocity, and pseudoangular momentum are analyzed. Based on their selective coupling with valley electrons and photons, we propose an experimental setup to detect the unique feature of propagating chiral phonons. Our work endows chiral phonons with a crucial character-the ability to propagate and transport quantized information, which creates a new research direction and opens up the possibility to design novel phononic quantum devices.

Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets

Upon strain, most materials shrink normal to the direction of applied strain. Similarly, if a material is compressed, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of stress, regardless if it is strained or compressed. Such behavior, namely, half-auxeticity, is demonstrated for a borophene sheet stabilized by decorating Pd atoms. We explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability and mechanical and electronic properties we explore the origin of this very uncommon behavior and identify it as a structural feature that may also be employed to design further 2D nanomaterials.

Coexistence of Ferroelectricity and Ferromagnetism in One-Dimensional SbN and BiN Nanowires

Ferroelectricity exists in a variety of three- and two-dimensional materials and is of great significance for the development of electronic devices. However, the presence of ferroelectricity in one-dimensional materials is extremely rare. Here, we predict ferroelectricity in one-dimensional SbN and BiN nanowires. Their polarization strengths are 1 order of magnitude higher than ever reported values in one-dimensional structures. Moreover, we find that spontaneous spin polarization can be generated in SbN and BiN nanowires by moderate hole doping. This is the first time the coexistence of both ferroelectricity and ferromagnetism in a one-dimensional system has been reported. Our finding not only broadens the family of one-dimensional ferroelectric materials but also offers a promising platform for novel electronic and spintronic applications.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Index Theorem on Chiral Landau Bands for Topological Fermions

Topological fermions as excitations from multidegenerate Fermi points have been attracting increasing interest in condensed matter physics. They are characterized by topological charges, and magnetic fields are usually applied in experiments for their detection. Here we present an index theorem that reveals the intrinsic connection between the topological charge of a Fermi point and the in-gap modes in the Landau band structure. The proof is based on mapping fermions under magnetic fields to a topological insulator whose topological number is exactly the topological charge of the Fermi point. Our Letter lays a solid foundation for the study of intriguing magnetoresponse effects of topological fermions.

A two-dimensional h-BN/C2N heterostructure as a promising metal-free photocatalyst for overall water-splitting

The construction of a heterostructure (HS) is an effective strategy to modulate the desired properties of two-dimensional (2D) materials and to extend their applications. In this paper, based on the density functional theory, we predict a metal-free type-II HS formed by h-BN and C₂N single layers. The h-BN/C₂N HS possesses a smaller bandgap than individual h-BN and C₂N single layers, and it exhibits excellent visible light absorption. Importantly, its band edge positions satisfy the requirements for spontaneous water-splitting. With the assistance of the built-in electric field across the HS and the band offset, the photoinduced carriers can be readily spatially separated. Free energy calculations indicate the high catalytic activity for water oxidation and reduction reactions. The performance can be further enhanced by strain, which modulates the bandgap and the band edge positions of the HS. The band alignment may undergo a transition from type-I to type-II under strain, offering an effective switch for the reaction. The appropriate bandgap, suitable band edge positions, and effective carrier separation make the h-BN/C₂N HS a promising candidate for use as a photocatalyst in water-splitting.

Visualizing the Anomalous Charge Density Wave States in Graphene/NbSe2 Heterostructures

Metallic layered transition metal dichalcogenides (TMDs) host collective many-body interactions, including the competing superconducting and charge density wave (CDW) states. Graphene is widely employed as a heteroepitaxial substrate for the growth of TMD layers and as an ohmic contact, where the graphene/TMD heterostructure is naturally formed. The presence of graphene can unpredictably influence the CDW order in 2D CDW conductors. This work reports the CDW transitions of 2H-NbSe₂ layers in graphene/NbSe₂ heterostructures. The evolution of Raman spectra demonstrates that the CDW phase transition temperatures (T_CDW ) of NbSe₂ are dramatically decreased when capped by graphene. The induced anomalous short-range CDW state is confirmed by scanning tunneling microscopy measurements. The findings propose a new criterion to determine the T_CDW through monitoring the line shape of the A_1g mode. Meanwhile, the 2D band is also discovered as an indicator to observe the CDW transitions. First-principles calculations imply that interfacial electron doping suppresses the CDW states by impeding the lattice distortion of 2H-NbSe₂ . The extraordinary random CDW lattice suggests deep insight into the formation mechanism of many collective electronic states and possesses great potential in modulating multifunctional devices.

Ideal Unconventional Weyl Point in a Chiral Photonic Metamaterial

Unconventional Weyl points (WPs), carrying topological charge 2 or higher, possess interesting properties different from ordinary charge-1 WPs, including multiple Fermi arcs that stretch over a large portion of the Brillouin zone. Thus far, such WPs have been observed in chiral materials and acoustic metamaterials, but there has been no clean demonstration in photonics in which the unconventional photonic WPs are separated from trivial bands. We experimentally realize an ideal symmetry-protected photonic charge-2 WP in a three-dimensional topological chiral microwave metamaterial. We use field mapping to directly observe the projected bulk dispersion, as well as the two long surface arcs that form a noncontractible loop wrapping around the surface Brillouin zone. The surface states span a record-wide frequency window of around 22.7% relative bandwidth. We demonstrate that the surface states exhibit a novel topological self-collimation property and are robust against disorder. This work provides an ideal photonic platform for exploring fundamental physics and applications of unconventional WPs.

Boundary Criticality of PT-Invariant Topology and Second-Order Nodal-Line Semimetals

For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present PT-invariant 2D topological insulators and 3D topological semimetals that go beyond this bulk-boundary correspondence framework. With unchanged bulk topological invariants, their first-order boundaries undergo transitions separating different phases with second-order boundary zero modes. For the 2D topological insulator, the helical edge modes appear at the transition point for two second-order topological insulator phases with diagonal and off-diagonal corner zero modes, respectively. Accordingly, for the 3D topological semimetal, the criticality corresponds to surface helical Fermi arcs of a Dirac semimetal phase. Interestingly, we find that the 3D system generically belongs to a novel second-order nodal-line semimetal phase, possessing gapped surfaces but a pair of diagonal or off-diagonal hinge Fermi arcs.

Plasmon of Au nanorods activates metal-organic frameworks for both the hydrogen evolution reaction and oxygen evolution reaction

Electrocatalytic water splitting holds great promise for renewable energy conversion and storage systems. However, it usually suffers from sluggish kinetics, which greatly hinders its real application. Here, we demonstrate the utilization of the localized surface plasmon resonance (LSPR) of Au nanorods (AuNRs) to significantly improve the electroactivity of both the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) at Co-MOF nanosheets (Co-MOFNs) under different polarizations. Theoretical calculations suggest that the HER enhancement can be largely attributed to the injection of hot electrons from plasmonic AuNRs to Co-MOFN catalysts, which upraises the Fermi level of Co-MOFNs, increasing their reductive activity towards the HER. Regarding the promotion of the OER, it is indicated that the formed holes in Co-MOFNs should majorly locate on the surface oxygen atoms, which may also serve as active positions working jointly with neighboring Co atoms in oxidizing OH-. The plasmon enhanced HER and OER electrocatalysis could also be observed over AuNR/Ni-MOFN and AuNR/NiCo-MOFN catalysts, suggesting the generality of this strategy. This study highlights the possibility of accelerating both the HER and OER efficiency by AuNR plasmonic excitation and provides a new route towards the design of more efficient water splitting systems with the assistance of light energy.

Ferroelectric control of single-molecule magnetism in 2D limit

The electric control of magnetic properties based on magnetoelectric effect is crucial for the development of future data storage devices. Here, based on first-principles calculations, a strong magnetoelectric effect is proposed to effectively switch on/off the magnetic states as well as alter the in-plane/perpendicular easy axes of metal-phthalocyanine molecules (MPc) by reversing the electric polarization of the underlying two-dimensional (2D) ferroelectric α-In₂Se₃ substrate with the application of an external electric field. The mechanism originates from the different hybridization between the molecule and the ferroelectric substrate in which the different electronic states of surface Se layer play a dominant role. Moreover, the magnetic moments and magnetic anisotropy energies (MAE) of OsPc/In₂Se₃ can be further largely enhanced by a functionalized atom atop the OsPc molecule. The I-OsPc/In₂Se₃ system possesses large MAE up to 30 meV at both polarization directions, which is sufficient for room-temperature applications. These findings provide a feasible scheme to realize ferroelectric control of magnetic states in 2D limit, which have great potential for applications in nanoscale electronics and spintronics.

Quantized Circulation of Anomalous Shift in Interface Reflection

A particle beam may undergo an anomalous spatial shift when it is reflected at an interface. The shift forms a vector field defined in the two-dimensional interface momentum space. We show that, although the shift vector at individual momentum is typically sensitive to the system details, its integral along a close loop, i.e., its circulation, could yield a robust quantized number under certain conditions of interest. Particularly, this is the case when the beam is incident from a trivial medium, then the quantized circulation of anomalous shift (CAS) directly manifests the topological character of the other medium. We demonstrate that the topological charge of a Weyl medium as well as the unconventional pair potentials of a superconductor can be captured and distinguished by CAS. Our work unveils a hidden quantized feature in a ubiquitous physical process, which may also offer a new approach for probing topological media.

Universal Approach to Magnetic Second-Order Topological Insulator

We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventional (first-order) topological insulators. The approach works for both three dimensions (3D) and two dimensions (2D), and is particularly suitable for 2D, where it can be achieved by coupling a quantum spin Hall insulator with a magnetic substrate. Using first-principles calculations, we predict bismuthene on EuO(111) surface as the first realistic system for a two-dimensional magnetic SOTI. We explicitly demonstrate the existence of the protected corner states. Benefitting from the large spin-orbit coupling and sizable magnetic proximity effect, these corner states are located in a boundary gap ∼83  meV, and hence can be readily probed in experiment. By controlling the magnetic phase transition, a topological phase transition between a first-order TI and a SOTI can be simultaneously achieved in the system. The effect of symmetry breaking, the connection with filling anomaly, and the experimental detection are discussed.