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.