Observation of the nonlinear Hall effect under time-reversal-symmetric conditions

Quantum-metric-induced nonlinear transport in a topological antiferromagnet

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

Topological Superconductors from a Materials Perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.

Anomalous Skew-Scattering Nonlinear Hall Effect and Chiral Photocurrents in PT-Symmetric Antiferromagnets

Berry curvature and skew scattering play central roles in determining both the linear and nonlinear anomalous Hall effects. Yet in PT-symmetric antiferromagnetic metals, Hall effects from either intrinsic Berry curvature mediated anomalous velocity or the conventional skew-scattering process individually vanish. Here we reveal an unexpected nonlinear Hall effect that relies on both Berry curvature and skew-scattering working in cooperation. This anomalous skew-scattering nonlinear Hall effect (ASN) is PT even and dominates the low-frequency nonlinear Hall effect for PT-symmetric antiferromagnetic metals. Surprisingly, we find that in addition to its Hall response, ASN produces helicity dependent photocurrents, in contrast to other known PT-even nonlinearities in metals that are helicity blind. This characteristic enables us to isolate ASN and establishes new photocurrent tools to interrogate the antiferromagnetic order of PT-symmetric metals.

Chiral Cation Doping for Modulating Structural Symmetry of 2D Perovskites

Cation mixing in two-dimensional (2D) hybrid organic-inorganic perovskite (HOIP) structures represents an important degree of freedom for modifying organic templating effects and tailoring inorganic structures. However, the limited number of known cation-mixed 2D HOIP systems generally employ a 1:1 cation ratio for stabilizing the 2D perovskite structure. Here, we demonstrate a chiral-chiral mixed-cation system wherein a controlled small amount (<10%) of chiral cation S-2-MeBA (S-2-MeBA = (S)-(-)-2-methylbutylammonium) can be doped into (S-BrMBA)2PbI4 (S-BrMBA = (S)-(-)-4-bromo-α-methylbenzylammonium), modulating the structural symmetry from a higher symmetry (C2) to the lowest symmetry state (P1). This structural change occurs when the concentration of S-2-MeBA, measured by solution nuclear magnetic resonance, exceeds a critical level─specifically, for 1.4 ± 0.6%, the structure remains as C2, whereas 3.9 ± 1.4% substitution induces the structure change to P1 (this structure is stable to ∼7% substitution). Atomic occupancy analysis suggests that one specific S-BrMBA cation site is preferentially substituted by S-2-MeBA in the unit cell. Density functional theory calculations indicate that the spin splitting along different k-paths can be modulated by cation doping. A true circular dichroism band at the exciton energy of the 3.9% doping phase shows polarity inversion and a ∼45 meV blue shift of the Cotton-effect-type line-shape relative to (S-BrMBA)2PbI4. A trend toward suppressed melting temperature with higher doping concentration is also noted. The chiral cation doping system and the associated doping-concentration-induced structural transition provide a material design strategy for modulating and enhancing those emergent properties that are sensitive to different types of symmetry breaking.

Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene

Though the observation of the quantum anomalous Hall effect and nonlocal transport response reveals nontrivial band topology governed by the Berry curvature in twisted bilayer graphene, some recent works reported nonlinear Hall signals in graphene superlattices that are caused by the extrinsic disorder scattering rather than the intrinsic Berry curvature dipole moment. In this Letter, we report a Berry curvature dipole induced intrinsic nonlinear Hall effect in high-quality twisted bilayer graphene devices. We also find that the application of the displacement field substantially changes the direction and amplitude of the nonlinear Hall voltages, as a result of a field-induced sliding of the Berry curvature hotspots. Our Letter not only proves that the Berry curvature dipole could play a dominant role in generating the intrinsic nonlinear Hall signal in graphene superlattices with low disorder densities, but also demonstrates twisted bilayer graphene to be a sensitive and fine-tunable platform for second harmonic generation and rectification.

Intrinsic Nonlinear Hall Detection of the Néel Vector for Two-Dimensional Antiferromagnetic Spintronics

The respective unique merit of antiferromagnets and two-dimensional (2D) materials in spintronic applications inspires us to exploit 2D antiferromagnetic spintronics. However, the detection of the Néel vector in 2D antiferromagnets remains a great challenge because the measured signals usually decrease significantly in the 2D limit. Here we propose that the Néel vector of 2D antiferromagnets can be efficiently detected by the intrinsic nonlinear Hall (INH) effect which exhibits unexpected significant signals. As a specific example, we show that the INH conductivity of the monolayer manganese chalcogenides MnX (X=S, Se, Te) can reach the order of nm·mA/V^{2}, which is orders of magnitude larger than experimental values of paradigmatic antiferromagnetic spintronic materials. The INH effect can be accurately controlled by shifting the chemical potential around the band edge, which is experimentally feasible via electric gating or charge doping. Moreover, we explicitly demonstrate its 2π-periodic dependence on the Néel vector orientation based on an effective k·p model. Our findings enable flexible design schemes and promising material platforms for spintronic memory device applications based on 2D antiferromagnets.

Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study demonstrates the potential for creating new functional moiré materials by incorporating intrinsic symmetry-breaking orders.

Berry curvature dipole generation and helicity-to-spin conversion at symmetry-mismatched heterointerfaces

The Berry curvature dipole (BCD) is a key parameter that describes the geometric nature of energy bands in solids. It defines the dipole-like distribution of Berry curvature in the band structure and plays a key role in emergent nonlinear phenomena. The theoretical rationale is that the BCD can be generated at certain symmetry-mismatched van der Waals heterointerfaces even though each material has no BCD in its band structure. However, experimental confirmation of such a BCD induced via breaking of the interfacial symmetry remains elusive. Here we demonstrate a universal strategy for BCD generation and observe BCD-induced gate-tunable spin-polarized photocurrent at WSe2/SiP interfaces. Although the rotational symmetry of each material prohibits the generation of spin photocurrent under normal incidence of light, we surprisingly observe a direction-selective spin photocurrent at the WSe2/SiP heterointerface with a twist angle of 0°, whose amplitude is electrically tunable with the BCD magnitude. Our results highlight a BCD-spin-valley correlation and provide a universal approach for engineering the geometric features of twisted heterointerfaces.

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi₂Te₄ with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

The Microscopic Mechanisms of Nonlinear Rectification on Si-MOSFETs Terahertz Detector

Studying the nonlinear photoresponse of different materials, including III-V semiconductors, two-dimensional materials and many others, is attracting burgeoning interest in the terahertz (THz) field. Especially, developing field-effect transistor (FET)-based THz detectors with preferred nonlinear plasma-wave mechanisms in terms of high sensitivity, compactness and low cost is a high priority for advancing performance imaging or communication systems in daily life. However, as THz detectors continue to shrink in size, the impact of the hot-electron effect on device performance is impossible to ignore, and the physical process of THz conversion remains elusive. To reveal the underlying microscopic mechanisms, we have implemented drift-diffusion/hydrodynamic models via a self-consistent finite-element solution to understand the dynamics of carriers at the channel and the device structure dependence. By considering the hot-electron effect and doping dependence in our model, the competitive behavior between the nonlinear rectification and hot electron-induced photothermoelectric effect is clearly presented, and it is found that the optimized source doping concentrations can be utilized to reduce the hot-electron effect on the devices. Our results not only provide guidance for further device optimization but can also be extended to other novel electronic systems for studying THz nonlinear rectification.

Designing spin and orbital sources of Berry curvature at oxide interfaces

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO₃/SrTiO₃ interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

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.

Valley-Hall alternatively changing conductivity in gapped and strained graphene

We investigated the alternatively changing (ac) valley-Hall effect in a graphene/h-BN structure under the modulations of a static electric field E₀, magnetic field B₀, and light field E_A1. The proximity to the h-BN film leads to a mass gap and strain-induced pseudopotential for electrons in graphene. Starting from the Boltzmann equation, we derive the ac conductivity tensor σ, including the orbital magnetic moment, Berry curvature, and anisotropic Berry curvature dipole. It is found that under B₀ ≠ 0, σ for the two valleys can have different amplitudes and even have the same sign, leading to a net ac Hall conductivity. The ac Hall conductivities and the optical gain can be altered by both the amplitude and the direction of E₀. These features can be understood from the changing rate of σ with E₀ and B₀, which is valley-resolved and varies nonlinearly with the chemical potential.

Geometry-Induced Spin Filtering in Photoemission Maps from WTe_{2} Surface States

We demonstrate that an important quantum material WTe_{2} exhibits a new type of geometry-induced spin filtering effect in photoemission, stemming from low symmetry that is responsible for its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted from the surface states of WTe_{2}. Such asymmetries are not present in the initial state spin textures, which are bound by the time-reversal and crystal lattice mirror plane symmetries. The findings are reproduced qualitatively by theoretical modeling within the one-step model photoemission formalism. The effect could be understood within the free-electron final state model as an interference due to emission from different atomic sites. The observed effect is a manifestation of time-reversal symmetry breaking of the initial state in the photoemission process, and as such it cannot be eliminated, but only its magnitude influenced, by special experimental geometries.

Giant Magnetochiral Anisotropy in Weyl Semimetal WTe_{2} Induced by Diverging Berry Curvature

The concept of Berry curvature is essential for various transport phenomena. However, an effect of the Berry curvature on magnetochiral anisotropy, i.e., nonreciprocal magnetotransport, is still elusive. Here, we report that the Berry curvature induces the large magnetochiral anisotropy. In Weyl semimetal WTe_{2}, we observe the strong enhancement of the magnetochiral anisotropy when the Fermi level is located near the Weyl points. Notably, the maximal figure of merit γ[over ¯] reaches 1.2×10^{-6}  m^{2} T^{-1} A^{-1}, which is the largest ever reported in bulk materials. Our semiclassical calculation shows that the diverging Berry curvature at the Weyl points strongly enhances the magnetochiral anisotropy.

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.

Ferroic Berry Curvature Dipole in a Topological Crystalline Insulator at Room Temperature

The physics related to Berry curvature is now a central research topic in condensed matter physics. The Berry curvature dipole (BCD) is a significant and intriguing condensed matter phenomenon that involves inversion symmetry breaking. However, the creation and controllability of BCDs have so far been limited to far below room temperature (RT), and nonvolatile (i.e., ferroic) BCDs have not yet been discovered, hindering further progress in topological physics. In this work, we demonstrate a switchable and nonvolatile BCD effect at RT in a topological crystalline insulator, Pb_1-xSn_xTe (PST), which is attributed to ferroic distortion. Surprisingly, the magnitude of the ferroic BCD is several orders of magnitude greater than that of the nonferroic BCDs that appear, for example, in transition metal dichalcogenides. The discovery of this ferroic and extraordinarily large BCD in PST could pave the way for further progress in topological materials science and the engineering of novel topological devices.

Terahertz Nonlinear Hall Rectifiers Based on Spin-Polarized Topological Electronic States in 1T-CoTe2

The zero-magnetic-field nonlinear Hall effect (NLHE) refers to the second-order transverse current induced by an applied alternating electric field; it indicates the topological properties of inversion-symmetry-breaking crystals. Despite several studies on the NLHE induced by the Berry-curvature dipole in Weyl semimetals, the direct current conversion by rectification is limited to very low driving frequencies and cryogenic temperatures. The nonlinear photoresponse generated by the NLHE at room temperature can be useful for numerous applications in communication, sensing, and photodetection across a high bandwidth. In this study, observations of the second-order NLHE in type-II Dirac semimetal CoTe₂ under time-reversal symmetry are reported. This is determined by the disorder-induced extrinsic contribution on the broken-inversion-symmetry surface and room-temperature terahertz rectification without the need for semiconductor junctions or bias voltage. It is shown that remarkable photoresponsivity over 0.1 A W^-1 , a response time of approximately 710 ns, and a mean noise equivalent power of 1 pW Hz^-1/2 can be achieved at room temperature. The results open a new pathway for low-energy photon harvesting via nonlinear rectification induced by the NLHE in strongly spin-orbit-coupled and inversion-symmetry-breaking systems, promising a considerable impact in the field of infrared/terahertz photonics.

Nonlinear Hall effect in monolayer phosphorene with broken inversion symmetry

Nonlinear Hall effect (NLHE), a new member of the family of Hall effects, in monolayer phosphorene is investigated. We find that phosphorene exhibits pronounced NLHE, arising from the dipole moment of the Berry curvature induced by the proximity effect that breaks the inversion symmetry of the system. Remarkably, the nonlinear Hall response exhibits central minimum with a width on the order of the band gap, followed by two resonance-like peaks. Interestingly, each resonance peak of the Hall response shifts in the negative region of the chemical potential which is consistent with the shift of valence and conduction bands in the energy spectrum of monolayer phosphorene. It is observed that the two peaks are asymmetric, originated from anisotropy in the band structure of phosphorene. It is shown that the NLHE is very sensitive to the band gap and temperature of the system. Moreover, we find that a phase transition occurs in the nonlinear Hall response and nonlinear spin Hall conductivity of the system under the influence of spin-orbit interaction, tuned by the strength of interaction and band gap induced in the energy spectrum of monolayer phosphorene with broken inversion symmetry.

Recent advances in 2D TMD circular photo-galvanic effects

Two-dimensional (2D) layered semiconductors are appealing materials for high-specific-power photovoltaic systems due to their unique optoelectronic properties. The 2D materials can be naturally thin, and their properties can be altered in a variety of ways. Therefore, these materials may be used to develop high-performance opto-spintronic and photovoltaic devices. The most recent and promising strategies were used to induce circular photo-galvanic effects (CPGEs) in 2D TMD materials with broken inversion symmetry. The majority of quantum devices were manufactured by mechanical exfoliation to investigate the electrical behavior of ultrathin 2D materials. The investigation of CPGEs in 2D materials could enable the exploration of spin-polarized optoelectronics to produce more energy-efficient computing systems. The current research on nanomaterial-based materials paves the way for developing materials to store, manipulate, and transmit information with better performance. Finally, this study concludes by summarizing the current challenges and prospects.

Electronic structure and layer-dependent magnetic order of a new high-mobility layered antiferromagnet KMnBi

Room-temperature two-dimensional antiferromagnetic (AFM) materials are highly desirable for various device applications. In this letter, we report the low-energy electronic structure of KMnBi measured by angle-resolved photoemission spectroscopy, which confirms an AFM ground state with the valence band maximum located at -100 meV below the Fermi level and small hole effective masses associated with the sharp band dispersion. Using complementary Raman, atomic force microscope and electric transport measurement, we systematically study the evolution of electric transport characteristics of micro-mechanically exfoliated KMnBi with varied flake thicknesses, which all consistently reveal the existence of a probable AFM ground state down to the quintuple-layer regime. The AFM phase transition temperature ranges from 220 K to 275 K, depending on the thickness. Our results suggest that with proper device encapsulation, multilayer KMnBi is indeed a promising 2D AFM platform for testing various theoretical proposals for device applications.

Engineering Transistorlike Optical Gain in Two-Dimensional Materials with Berry Curvature Dipoles

Transistors are key elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, we use the semiclassical Boltzmann equation approach to characterize the optical conductivity of a two-dimensional material under a static electric bias. Similar to the nonlinear Hall effect, the linear electro-optic (EO) response depends on the Berry curvature dipole and can lead to nonreciprocal optical interactions. Most interestingly, our analysis uncovers a novel non-Hermitian linear EO effect that can lead to optical gain and to a distributed transistor response. We study a possible realization based on strained bilayer graphene. Our analysis reveals that the optical gain for incident light transmitted through the biased system depends on the light polarization, and can be quite large, especially for multilayer configurations.

All-electrical switching of a topological non-collinear antiferromagnet at room temperature

Non-collinear antiferromagnetic Weyl semimetals, combining the advantages of a zero stray field and ultrafast spin dynamics, as well as a large anomalous Hall effect and the chiral anomaly of Weyl fermions, have attracted extensive interest. However, the all-electrical control of such systems at room temperature, a crucial step toward practical application, has not been reported. Here, using a small writing current density of around 5 × 10⁶ A·cm^-2, we realize the all-electrical current-induced deterministic switching of the non-collinear antiferromagnet Mn₃Sn, with a strong readout signal at room temperature in the Si/SiO₂/Mn₃Sn/AlO_x structure, and without external magnetic field or injected spin current. Our simulations reveal that the switching originates from the current-induced intrinsic non-collinear spin-orbit torques in Mn₃Sn itself. Our findings pave the way for the development of topological antiferromagnetic spintronics.

Strong room-temperature bulk nonlinear Hall effect in a spin-valley locked Dirac material

Nonlinear Hall effect (NLHE) is a new type of Hall effect with wide application prospects. Practical device applications require strong NLHE at room temperature (RT). However, previously reported NLHEs are all low-temperature phenomena except for the surface NLHE of TaIrTe4. Bulk RT NLHE is highly desired due to its ability to generate large photocurrent. Here, we show the spin-valley locked Dirac state in BaMnSb2 can generate a strong bulk NLHE at RT. In the microscale devices, we observe the typical signature of an intrinsic NLHE, i.e. the transverse Hall voltage quadratically scales with the longitudinal current as the current is applied to the Berry curvature dipole direction. Furthermore, we also demonstrate our nonlinear Hall device's functionality in wireless microwave detection and frequency doubling. These findings broaden the coupled spin and valley physics from 2D systems into a 3D system and lay a foundation for exploring bulk NLHE's applications.

Quantum Fluctuation of the Quantum Geometric Tensor and Its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems

In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying the quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects; so do their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is purely intrinsic, and the second-order thermal Hall noise has both intrinsic and extrinsic contributions. In particular, the intrinsic part of the second-order thermal Hall noise is a manifestation of the quantum fluctuation of the quantum geometric tensor, which widely exists as long as Berry curvature is nonzero. These intrinsic thermal Hall noises provide direct measurable means to band geometric information, including Berry curvature related quantities and quantum fluctuation of quantum geometric tensor.

Probing magnetic orbitals and Berry curvature with circular dichroism in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at selected atoms in materials, including particle-hole transitions between the valence and conduction bands. These transitions are governed by fundamental properties of the corresponding Bloch wave functions, including orbital and magnetic degrees of freedom, and quantum geometric properties such as the Berry curvature. In particular, orbital angular momentum (OAM), which is closely linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We demonstrate how information on such OAM textures can be extracted from the circular dichroism in RIXS. Based on accurate modeling with a first-principles treatment of the key ingredient-the light-matter interaction-we simulate dichroic RIXS spectra for the prototypical transition-metal dichalcogenide MoSe2 and the two-dimensional topological insulator 1T'-MoS2. Guided by an intuitive picture of the optical selection rules, we discuss how the momentum-dependent OAM manifests itself in the dichroic RIXS signal if one controls the momentum transfer. Our calculations are performed for typical experimental geometries and parameter regimes, and demonstrate the possibility of observing the predicted circular dichroism in forthcoming experiments. Thus, our work establishes a new avenue for observing Berry curvature and topological states in quantum materials.

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.

Investigating active area dependent high performing photoresponse through thin films of Weyl Semimetal WTe2

WTe₂ is one of the wonder layered materials, displays interesting overlapping of electron-hole pairs, opening of the surface bandgap, anisotropy in its crystal structure and very much sought appealing material for room temperature broadband photodection applications. Here we report the photoresponse of WTe₂ thin films and microchannel devices fabricated on silicon nitride substrates. A clear sharp rise in photocurrent observed under the illumination of visible (532 nm) and NIR wavelengths (1064 nm). The observed phoresponse is very convincing and repetitive for ON /OFF cycles of laser light illumination. The channel length dependence of photocurrent is noticed for few hundred nanometers to micrometers. The photocurrent, rise & decay times, responsivity and detectivity are studied using different channel lengths. Strikingly microchannel gives few orders of greater responsivity compared to larger active area investigated here. The responsivity and detectivity are observed as large as 29 A/W and 3.6 × 10⁸ Jones respectively. The high performing photodetection properties indicate that WTe₂ can be used as a broad band material for future optoelectronic applications.

Giant photon momentum locked THz emission in a centrosymmetric Dirac semimetal

Strong second-order optical nonlinearities often require broken material centrosymmetry, thereby limiting the type and quality of materials used for nonlinear optical devices. Here, we report a giant and highly tunable terahertz (THz) emission from thin polycrystalline films of the centrosymmetric Dirac semimetal PtSe₂. Our PtSe₂ THz emission is turned on at oblique incidence and locked to the photon momentum of the incident pump beam. Notably, we find an emitted THz efficiency that is giant: It is two orders of magnitude larger than the standard THz-generating nonlinear crystal ZnTe and has values approaching that of the noncentrosymmetric topological material TaAs. Further, PtSe₂ THz emission displays THz sign and amplitude that is controlled by the incident pump polarization and helicity state even as optical absorption is only weakly polarization dependent and helicity independent. Our work demonstrates how photon drag can activate pronounced optical nonlinearities that are available even in centrosymmetric Dirac materials.

Emergent Magnetomultipoles and Nonlinear Responses of a Magnetic Hopfion

The three-dimensional emergent magnetic field B^{e} of a magnetic hopfion gives rise to emergent magnetomultipoles in a similar manner to the multipoles of classical electromagnetic field. Here, we show that the nonlinear responses of a hopfion are characterized by its emergent magnetic toroidal moment T_{z}^{e}=1/2∫(r×B^{e})_{z}dV and emergent magnetic octupole component Γ^{e}=∫[(x^{2}+y^{2})B_{z}^{e}-xzB_{x}^{e}-yzB_{y}^{e}]dV. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along (perpendicular to) the direction of T_{z}^{e}. The sign of nonreciprocity and nonlinear Hall angle is determined by the polarity and chirality of hopfion. The nonlinear electrical transport induced by a magnetic hopfion is also discussed. This Letter reveals the vital roles of emergent magnetomultipoles in nonlinear hopfion dynamics and could stimulate further investigations on the dynamical responses of topological spin textures induced by emergent electromagnetic multipoles.

Influence of strain on an ultrafast phase transition

The flexibility of 2D materials combined with properties highly sensitive to strain makes strain engineering a promising avenue for manipulation of both structure and function. Here we investigate the influence of strain, associated with microstructural defects, on a photo-induced structural phase transition in Td-WTe₂. Above threshold photoexcitation of uniform, non-strained, samples result in an orthorhombic Td to a metastable orthorhombic 1T* phase transition facilitated by shear displacements of the WTe₂ layers along the b axis of the material. In samples prepared with wrinkle defects WTe₂ continue its trajectory through a secondary transition that shears the unit cell along the c axis towards a metastable monoclinic 1T' phase. The time scales and microstructural evolution associated with the transition and its subsequent recovery to the 1T* phase is followed in detail by a combination of ultrafast electron diffraction and microscopy. Our findings show how local strain fields can be employed for tailoring phase change dynamics in ultrafast optically driven processes with potential applications in phase change devices.

Breaking of Inversion Symmetry and Interlayer Electronic Coupling in Bilayer Graphene Heterostructure by Structural Implementation of High Electric Displacement Fields

Controlling the interlayer coupling in two-dimensional (2D) materials generates novel electronic and topological phases. Its effective implementation is commonly done with a transverse electric field. However, phases generated by high displacement fields are elusive in this standard approach. Here, we introduce an exceptionally large displacement field by structural modification of a model system: AB-stacked bilayer graphene (BLG) on a SiC(0001) surface. We show that upon intercalation of gadolinium, electronic states in the top graphene layers exhibit a significant difference in the on-site potential energy, which effectively breaks the interlayer coupling between them. As a result, for energies close to the corresponding Dirac points, the BLG system behaves like two electronically isolated single graphene layers. This is proven by local scanning tunneling microscopy (STM)/spectroscopy, corroborated by density functional theory, tight binding, and multiprobe STM transport. The work presents metal intercalation as a promising approach for the synthesis of 2D graphene heterostructures with electronic phases generated by giant displacement fields.

Breaking Rotational Symmetry in Supertwisted WS2 Spirals via Moiré Magnification of Intrinsic Heterostrain

Twisted stacking of van der Waals materials with moiré superlattices offers a new way to tailor their physical properties via engineering of the crystal symmetry. Unlike well-studied twisted bilayers, little is known about the overall symmetry and symmetry-driven physical properties of continuously supertwisted multilayer structures. Here, using polarization-resolved second harmonic generation (SHG) microscopy, we report threefold (C3) rotational symmetry breaking in supertwisted WS2 spirals grown on non-Euclidean surfaces, contrasting the intact symmetry of individual monolayers. This symmetry breaking is attributed to a geometrical magnifying effect in which small relative strain between adjacent twisted layers (heterostrain), verified by Raman spectroscopy and multiphysics simulations, generates significant distortion in the moiré pattern. Density-functional theory calculations can explain the C3 symmetry breaking and unusual SHG response by the interlayer wave function coupling. These findings thus pave the way for further developments in the so-called "3D twistronics".

Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vector-like, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z₂× Z₂× Z₂group with Abelian additive operation, and the cross products form a Z₂× Z₂group with Abelian additive operation or Q₈, a non-Abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has symmetry operational similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.

Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene

In the second-order response regime, the Hall voltage can be nonzero without time-reversal symmetry breaking but inversion symmetry breaking. Multiple mechanisms contribute to the nonlinear Hall effect. The disorder-related contributions can enter the NLHE in the leading role, but experimental investigations are scarce, especially the exploration of the contributions from different disorder sources. Here, we report a giant nonlinear response in twisted bilayer graphene, dominated by disorder-induced skew scattering. The magnitude and direction of the second-order nonlinearity can be effectively tuned by the gate voltage. A peak value of the second-order Hall conductivity reaching 8.76  μm SV^{-1} is observed close to the full filling of the moiré band, four order larger than the intrinsic contribution detected in WTe_{2}. The scaling shows that the giant second-order nonlinear Hall effect in twisted bilayer graphene stems from the collaboration of the static (impurities) and dynamic (phonons) disorders. It is mainly determined by the impurity skew scattering at 1.7 K. The phonon skew scattering, however, has a much larger coupling coefficient, and becomes comparable to the impurity contribution as the temperature rises. Our observations provide a comprehensive experimental understanding of the disorder-related mechanisms in the nonlinear Hall effect.

Ferroelectricity-Driven Phonon Berry Curvature and Nonlinear Phonon Hall Transports

Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable nonlinear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the nonvolatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges and opens a mass gap in tilted Weyl phonon modes, resulting in a large phonon BC dipole. Furthermore, our ab initio non-equilibrium molecular dynamics simulations reveal that nonlinear phonon Hall transport occurs in a controllable manner via ferroelectric switching. The ferroelectricity-driven phonon BC and corresponding nonlinear phonon transports provide a novel scheme for constructing topological phononic transport/memory devices.

Ultrasensitive Anisotropic Room-Temperature Terahertz Photodetector Based on an Intrinsic Magnetic Topological Insulator MnBi2Te4

Terahertz photodetectors based on emergent intrinsic magnetic topological insulators promise excellent performance in terms of highly sensitive, anisotropic and room-temperature ability benefiting from their extraordinary material properties. Here, we propose and conceive the response features of exfoliated MnBi₂Te₄ flakes as active materials for terahertz detectors. The MnBi₂Te₄-based photodetectors show the sensitivity rival with commercially available ones, and the noise equivalent power of 13 pW/Hz^0.5 under 0.275 THz at room-temperature led by the nonlinear Hall effect, allowing for the high-resolution terahertz imaging. In addition, a large anisotropy of polarization-dependent terahertz response is observed when the MnBi₂Te₄ device is tuned into different directions. More interestingly, we discover an unprecedented power-controlled reversal of terahertz response in the MnBi₂Te₄-graphene device. Our results provide feasibility of manipulating and exploiting the nontrivial topological phenomena of MnBi₂Te₄ under a high-frequency electromagnetic field, representing the first step toward device implementation of intrinsic magnetic topological insulators.

Growth of bilayer MoTe2 single crystals with strong non-linear Hall effect

The reduced symmetry in strong spin-orbit coupling materials such as transition metal ditellurides (TMDTs) gives rise to non-trivial topology, unique spin texture, and large charge-to-spin conversion efficiencies. Bilayer TMDTs are non-centrosymmetric and have unique topological properties compared to monolayer or trilayer, but a controllable way to prepare bilayer MoTe₂ crystal has not been achieved to date. Herein, we achieve the layer-by-layer growth of large-area bilayer and trilayer 1T′ MoTe₂ single crystals and centimetre-scale films by a two-stage chemical vapor deposition process. The as-grown bilayer MoTe₂ shows out-of-plane ferroelectric polarization, whereas the monolayer and trilayer crystals are non-polar. In addition, we observed large in-plane nonlinear Hall (NLH) effect for the bilayer and trilayer T_d phase MoTe₂ under time reversal-symmetric conditions, while these vanish for thicker layers. For a fixed input current, bilayer T_d MoTe₂ produces the largest second harmonic output voltage among the thicker crystals tested. Our work therefore highlights the importance of thickness-dependent Berry curvature effects in TMDTs that are underscored by the ability to grow thickness-precise layers.

2D transition metal ditellurides exhibit nontrivial topological phases, but the controlled bottom-up synthesis of these materials is still challenging. Here, the authors report the layer-by-layer growth of large-area bilayer and trilayer 1T’ MoTe2 films, showing thickness-dependent ferroelectricity and nonlinear Hall effect.

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.

Non-linear Hall effect in multi-Weyl semimetals

In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate the Berry curvature induced second and third order Hall effect in multi-Weyl semimetals with topological chargesn=1,2,3. We use low energy effective models to obtain general analytical expressions and discover the presence of a large Berry curvature dipole (BCD) in multi-Weyl semimetals, compared to usual (n = 1) Weyl semimetals. We also study the BCD in a realistic tight-binding lattice model and observe two different kinds of variation with increasing topological charge-these can be attributed to different underlying Berry curvature components. We provide estimates of the signatures of second harmonic of Hall signal in multi-Weyl semimetals, which can be detected experimentally. Furthermore, we predict the existence of a third order Hall signal in multi-Weyl semimetals. We derive the analytical expressions of Berry connection polarizability tensor, which is responsible for third order effects, using a low energy model and estimate the measurable conductivity. Our work can help guide experimental discovery of Berry curvature multipole physics in multi-Weyl semimetals.

Terahertz wave emission from the trigonal layered PtBi2

In this work, broadband terahertz (THz) wave emissions have been detected from the trigonal layered PtBi₂ on the excitation of the femtosecond laser pulses. Such THz generation is found to arise from the dominated linear photogalvanic effect, which is further discovered to strongly depend on the unique electronic structures of PtBi₂. Furthermore, an effective nonlinear susceptibility of PtBi₂ is also obtained and is nearly two orders of magnitude larger than that of the traditional nonlinear crystal for THz generation.

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Terahertz (THz) wave emission, topological semimetal, ultrafast photocurrent

Berry curvature-induced local spin polarisation in gated graphene/WTe2 heterostructures

Experimental control of local spin-charge interconversion is of primary interest for spintronics. Van der Waals (vdW) heterostructures combining graphene with a strongly spin-orbit coupled two-dimensional (2D) material enable such functionality by design. Electric spin valve experiments have thus far provided global information on such devices, while leaving the local interplay between symmetry breaking, charge flow across the heterointerface and aspects of topology unexplored. Here, we probe the gate-tunable local spin polarisation in current-driven graphene/WTe₂ heterostructures through magneto-optical Kerr microscopy. Even for a nominal in-plane transport, substantial out-of-plane spin accumulation is induced by a corresponding out-of-plane current flow. We present a theoretical model which fully explains the gate- and bias-dependent onset and spatial distribution of the intense Kerr signal as a result of a non-linear anomalous Hall effect in the heterostructure, which is enabled by its reduced point group symmetry. Our findings unravel the potential of 2D heterostructure engineering for harnessing topological phenomena for spintronics, and constitute an important step toward nanoscale, electrical spin control.

Spin-based electronics offers significantly improved efficiency, but a major challenge is the electric manipulation of spin. Here, Powalla et al find a large gate induced spinpolarization in graphene/WTe2 heterostructures, illustrating the potential of such heterostructures for spintronics.

Nonlinear Optical and Photocurrent Responses in Janus MoSSe Monolayer and MoS2-MoSSe van der Waals Heterostructure

Two-dimensional (2D) transition metal dichalcogenides are promising materials platforms for a variety of optoelectronic device applications. Janus 2D materials are a rising class of 2D materials with low symmetry, which leads to the emergence of out-of-plane electric polarization and piezoelectricity. Using first-principles density functional theory, we show that monolayer and bilayer heterostructure Janus MoSSe moieties exhibit strong nonlinear optical responses that are vanishing in the non-Janus form. The absence of horizontal mirror plane symmetry enables a circular photocurrent as well as a large out-of-plane second harmonic generation (SHG) and shift photocurrent. Through a comparative study of the Janus heterostructure MoS₂-MoSSe on five distinct stacking configurations, we find that the magnitude of the out-of-plane SHG in the Janus heterostructure is enhanced due to the interlayer coupling and interference effect compared to that of monolayer MoSSe. Thus, Janus 2D materials offer a unique opportunity for exploring nonlinear optical phenomena and designing configurable layered nonlinear optical materials.

Determination of Cleavage Energy and Efficient Nanostructuring of Layered Materials by Atomic Force Microscopy

A method is presented to use atomic force microscopy to measure the cleavage energy of van der Waals materials and similar quasi-two-dimensional materials. The cleavage energy of graphite is measured to be 0.36 J/m², in good agreement with literature data. The same method yields a cleavage energy of 0.6 J/m² for MoS₂ as a representative of the dichalcogenides. In the case of the weak topological insulator Bi₁₄Rh₃I₉ no cleavage energy is obtained, although cleavage is successful with an adapted approach. The cleavage energies of these materials are evaluated by means of density-functional calculations and literature data. This further validates the presented method and sets an upper limit of about 0.7 J/m² to the cleavage energy that can be measured by the present setup. In addition, this method can be used as a tool for manipulating exfoliated flakes, prior to or after contacting, which may open a new route for the fabrication of nanostructures.

Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires

Chiral materials are an ideal playground for exploring the relation between symmetry, relativistic effects and electronic transport. For instance, chiral organic molecules have been intensively studied to electrically generate spin-polarized currents in the last decade, but their poor electronic conductivity limits their potential for applications. Conversely, chiral inorganic materials such as tellurium have excellent electrical conductivity, but their potential for enabling the electrical control of spin polarization in devices remains unclear. Here, we demonstrate the all-electrical generation, manipulation and detection of spin polarization in chiral single-crystalline tellurium nanowires. By recording a large (up to 7%) and chirality-dependent unidirectional magnetoresistance, we show that the orientation of the electrically generated spin polarization is determined by the nanowire handedness and uniquely follows the current direction, while its magnitude can be manipulated by an electrostatic gate. Our results pave the way for the development of magnet-free chirality-based spintronic devices.

Insights into the Interactions Between Root Phenotypic Traits and the Rhizosphere Bacterial Community

The root phenotypic traits have been considered as important factors in shaping the rhizosphere microbiome and regulating plant growth. However, the relationships between root phenotypic traits and the rhizosphere bacterial community remain unclear. We investigated two fields with different developing tobacco roots by a long-term positioning test in Hengshi. The well-developed root system (WDR) showed much more superiority in root phenotypic traits, including total root length, total projection area, surface area, and root tip number, than the underdeveloped root system. The specific root traits in WDR provided more ecological niches for the rhizosphere microorganisms, contributing to a more diverse microbial community and a more complex microbial network. The total root length and root tip number were the key factors shaping bacterial communities in the rhizosphere. In turn, the phyla Acidobacteria and Bacteroidetes might play vital roles in modifying root development and promoting plant growth according to their positive correlation with root phenotypic traits. Linking root phenotypic traits to the microbiome may enhance our understanding of rhizospheric interactions and their roles in developing rhizosphere ecosystems.

Graphene moiré superlattices with giant quantum nonlinearity of chiral Bloch electrons

Graphene-based samples have shown a plethora of exotic characteristics and these properties may help the realization of a new generation of fast electronic devices. However, graphene's centrosymmetry prohibits second-order electronic transport. Here, we show giant second-order nonlinear transports in graphene moiré superlattices at zero magnetic field, both longitudinal and transverse to the applied current direction. High carrier mobility and inversion symmetry breaking by hexagonal boron nitride lead to nonlinear conductivities five orders of magnitude larger than those in WTe₂. The nonlinear conductivity strongly depends on the gate voltage as well as on the stacking configuration, with a giant enhancement originating from the moiré bands. Longitudinal nonlinear conductivity cannot originate from Berry curvature dipoles. Our theoretical modelling highlights skew scattering of chiral Bloch electrons as the physical origin. With these results, we demonstrate nonlinear charge transport due to valley-contrasting chirality, which constitutes an alternative means to induce second-order transports in van der Waals heterostructures. Our approach is promising for applications in frequency-doubling and energy harvesting via rectification.

Emerging Phases of Layered Metal Chalcogenides

Layered metal chalcogenides, as a "rich" family of 2D materials, have attracted increasing research interest due to the abundant choices of materials with diverse structures and rich electronic characteristics. Although the common metal chalcogenide phases such as 2H and 1T have been intensively studied, many other unusual phases are rarely explored, and some of these show fascinating behaviors including superconductivity, ferroelectrics, ferromagnetism, etc. From this perspective, the unusual phases of metal chalcogenides and their characteristics, as well as potential applications are introduced. First, the unusual phases of metal chalcogenides from different classes, including transition metal dichalcogenides, magnetic element-based chalcogenides, and metal phosphorus chalcogenides, are discussed, respectively. Meanwhile, their excellent properties of different unusual phases are introduced. Then, the methods for producing the unusual phases are discussed, specifically, the stabilization strategies during the chemical vapor deposition process for the unusual phase growth are discussed, followed by an outlook and discussions on how to prepare the unusual phase metal dichalcogenides in terms of synthetic methodology and potential applications.

Giant second harmonic transport under time-reversal symmetry in a trigonal superconductor

Nonreciprocal or even-order nonlinear responses in symmetry-broken systems are powerful probes of emergent properties in quantum materials, including superconductors, magnets, and topological materials. Recently, vortex matter has been recognized as a key ingredient of giant nonlinear responses in superconductors with broken inversion symmetry. However, nonlinear effects have been probed as excess voltage only under broken time-reversal symmetry. In this study, we report second harmonic transport under time-reversal symmetry in the noncentrosymmetric trigonal superconductor PbTaSe₂. The magnitude of anomalous nonlinear transport is two orders of magnitude larger than those in the normal state, and the directional dependence of nonlinear signals are fully consistent with crystal symmetry. The enhanced nonlinearity is semiquantitatively explained by the asymmetric Hall effect of vortex-antivortex string pairs in noncentrosymmetric systems. This study enriches the literature on nonlinear phenomena by elucidating quantum transport in noncentrosymmetric superconductors.

Even-order nonlinear transport is a powerful probe of quantum materials, but such studies in superconductors have been limited to those which break time-reversal symmetry. Here, the authors observe second-order nonlinear transport in time-reversal-symmetric PbTaSe₂, where the nonlinearity is enhanced in the superconducting state.

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.