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.

Ultrathin quantum light source with van der Waals NbOCl2 crystal.

Interlayer electronic coupling in two-dimensional materials enables tunable and emergent properties by stacking engineering. However, it also results in significant evolution of electronic structures and attenuation of excitonic effects in two-dimensional semiconductors as exemplified by quickly degrading excitonic photoluminescence and optical nonlinearities in transition metal dichalcogenides when monolayers are stacked into van der Waals structures. Here we report a van der Waals crystal, niobium oxide dichloride (NbOCl2), featuring vanishing interlayer electronic coupling and monolayer-like excitonic behaviour in the bulk form, along with a scalable second-harmonic generation intensity of up to three orders higher than that in monolayer WS2. Notably, the strong second-order nonlinearity enables correlated parametric photon pair generation, through a spontaneous parametric down-conversion (SPDC) process, in flakes as thin as about 46 nm. To our knowledge, this is the first SPDC source unambiguously demonstrated in two-dimensional layered materials, and the thinnest SPDC source ever reported. Our work opens an avenue towards developing van der Waals material-based ultracompact on-chip SPDC sources as well as high-performance photon modulators in both classical and quantum optical technologies1-4.

Topological Chern vectors in three-dimensional photonic crystals.

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, 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-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. 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.

Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5.

The discovery of the quantum Hall effect (QHE)1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. Although the possibility of generalizing the QHE to three-dimensional (3D) electronic systems3,4 was proposed decades ago, it has not been demonstrated experimentally. Here we report the experimental realization of the 3D QHE in bulk zirconium pentatelluride (ZrTe5) crystals. We perform low-temperature electric-transport measurements on bulk ZrTe5 crystals under a magnetic field and achieve the extreme quantum limit, where only the lowest Landau level is occupied, at relatively low magnetic fields. In this regime, we observe a dissipationless longitudinal resistivity close to zero, accompanied by a well-developed Hall resistivity plateau proportional to half of the Fermi wavelength along the field direction. This response is the signature of the 3D QHE and strongly suggests a Fermi surface instability driven by enhanced interaction effects in the extreme quantum limit. By further increasing the magnetic field, both the longitudinal and Hall resistivity increase considerably and display a metal-insulator transition, which represents another magnetic-field-driven quantum phase transition. Our findings provide experimental evidence of the 3D QHE and a promising platform for further exploration of exotic quantum phases and transitions in 3D systems.

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.

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.

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%.

Electric-field-tuned topological phase transition in ultrathin Na3Bi.

The electric-field-induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor1-4. In this scheme, 'on' is the ballistic flow of charge and spin along dissipationless edges of a two-dimensional quantum spin Hall insulator5-9, and 'off' is produced by applying an electric field that converts the exotic insulator to a conventional insulator with no conductive channels. Such a topological transistor is promising for low-energy logic circuits4, which would necessitate electric-field-switched materials with conventional and topological bandgaps much greater than the thermal energy at room temperature, substantially greater than proposed so far6-8. Topological Dirac semimetals are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases3,10-16. Here we use scanning tunnelling microscopy and spectroscopy and angle-resolved photoelectron spectroscopy to show that mono- and bilayer films of the topological Dirac semimetal3,17 Na3Bi are two-dimensional topological insulators with bulk bandgaps greater than 300 millielectronvolts owing to quantum confinement in the absence of electric field. On application of electric field by doping with potassium or by close approach of the scanning tunnelling microscope tip, the Stark effect completely closes the bandgap and re-opens it as a conventional gap of 90 millielectronvolts. The large bandgaps in both the conventional and quantum spin Hall phases, much greater than the thermal energy at room temperature (25 millielectronvolts), suggest that ultrathin Na3Bi is suitable for room-temperature topological transistor operation.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.