Room-temperature nonlinear Hall effect and wireless radiofrequency rectification in Weyl semimetal TaIrTe4

Giant nonlinear Hall and wireless rectification effects at room temperature in the elemental semiconductor tellurium

The second-order nonlinear Hall effect (NLHE) in non-centrosymmetric materials has recently drawn intense interest, since its inherent rectification could enable various device applications such as energy harvesting and wireless charging. However, previously reported NLHE systems normally suffer from relatively small Hall voltage outputs and/or low working temperatures. In this study, we report the observation of a pronounced NLHE in tellurium (Te) thin flakes at room temperature. Benefiting from the semiconductor nature of Te, the obtained nonlinear response can be readily enhanced through electrostatic gating, leading to a second-harmonic output at 300 K up to 2.8 mV. By utilizing such a giant NLHE, we further demonstrate the potential of Te as a wireless Hall rectifier within the radiofrequency range, which is manifested by the remarkable and tunable rectification effect also at room temperature. Extrinsic scattering is then revealed to be the dominant mechanism for the NLHE in Te, with symmetry breaking on the surface playing a key role. As a simple elemental semiconductor, Te provides an appealing platform to advance our understanding of nonlinear transport in solids and to develop NLHE-based electronic devices.

Two-dimensional topological semimetals: an emerging candidate for terahertz detectors and on-chip integration

The importance of terahertz (THz) detection lies in its ability to provide detailed information in a non-destructive manner, making it a valuable tool across various domains including spectroscopy, communication, and security. The ongoing development of THz detectors aims to enhance their sensitivity, resolution and integration into compact and portable devices such as handheld scanners or integrated communication chips. Generally, two-dimensional (2D) materials are considered potential candidates for device miniaturization but detecting THz radiation using 2D semiconductors is generally difficult due to the ultra-small photon energy. However, this challenge is being addressed by the advent of topological semimetals (TSM) with zero-bandgap characteristics. These semimetals offer low-energy excitations in proximity to the Dirac point, which is particularly important for applications requiring a broad detection range. Their distinctive band structures with linear energy-momentum dispersion near the Fermi level also lead to high electron mobility and low effective mass. The presence of topologically protected dissipationless conducting channels and self-powered response provides a basis for low-energy integration. In order to establish paradigms for semimetal-based THz detectors, this review initially offers an analytical summary of THz detection principles. Then, the review demonstrates the distinct design of devices, the excellent performance derived from the topological surface state and unique band structures in TSM. Finally, we outline the prospective avenues for on-chip integration of TSM-based THz detectors. We believe this review can promote further research on the new generation of THz detectors and facilitate advancements in THz imaging, spectroscopy, and communication systems.

Microscale Chiral Rectennas for Energy Harvesting

Wireless radiofrequency rectifiers have the potential to power the billions of "Internet of Things" (IoT) devices currently in use by effectively harnessing ambient electromagnetic radiation. However, the current technology relies on the implementation of rectifiers based on Schottky diodes, which exhibit limited capabilities for high-frequency and low-power applications. Consequently, they require an antenna to capture the incoming signal and amplify the input power, thereby limiting the possibility of miniaturizing devices to the millimeter scale. Here, the authors report wireless rectification at the GHz range in a microscale device built on single chiral tellurium with extremely low input powers. By studying the crystal symmetry and the temperature dependence of the rectification, the authors demonstrate that its origin is the intrinsic nonlinear conductivity of the material. Additionally, the unprecedented ability to modulate the rectification output by an electrostatic gate is shown. These results open the path to developing tuneable microscale wireless rectifiers with a single material.

Large out-of-plane spin-orbit torque in topological Weyl semimetal TaIrTe4

The unique electronic properties of topological quantum materials, such as protected surface states and exotic quasiparticles, can provide an out-of-plane spin-polarized current needed for external field-free magnetization switching of magnets with perpendicular magnetic anisotropy. Conventional spin-orbit torque (SOT) materials provide only an in-plane spin-polarized current, and recently explored materials with lower crystal symmetries provide very low out-of-plane spin-polarized current components, which are not suitable for energy-efficient SOT applications. Here, we demonstrate a large out-of-plane damping-like SOT at room temperature using the topological Weyl semimetal candidate TaIrTe4 with a lower crystal symmetry. We performed spin-torque ferromagnetic resonance (STFMR) and second harmonic Hall measurements on devices based on TaIrTe4/Ni80Fe20 heterostructures and observed a large out-of-plane damping-like SOT efficiency. The out-of-plane spin Hall conductivity is estimated to be (4.05 ± 0.23)×104 (ℏ ⁄ 2e) (Ωm)-1, which is an order of magnitude higher than the reported values in other materials.

Spin-orbit-splitting-driven nonlinear Hall effect in NbIrTe4

The Berry curvature dipole (BCD) serves as a one of the fundamental contributors to emergence of the nonlinear Hall effect (NLHE). Despite intense interest due to its potential for new technologies reaching beyond the quantum efficiency limit, the interplay between BCD and NLHE has been barely understood yet in the absence of a systematic study on the electronic band structure. Here, we report NLHE realized in NbIrTe4 that persists above room temperature coupled with a sign change in the Hall conductivity at 150 K. First-principles calculations combined with angle-resolved photoemission spectroscopy (ARPES) measurements show that BCD tuned by the partial occupancy of spin-orbit split bands via temperature is responsible for the temperature-dependent NLHE. Our findings highlight the correlation between BCD and the electronic band structure, providing a viable route to create and engineer the non-trivial Hall effect by tuning the geometric properties of quasiparticles in transition-metal chalcogen compounds.

Observation of giant non-reciprocal charge transport from quantum Hall states in a topological insulator

Symmetry breaking in quantum materials is of great importance and can lead to non-reciprocal charge transport. Topological insulators provide a unique platform to study non-reciprocal charge transport due to their surface states, especially quantum Hall states under an external magnetic field. Here we report the observation of non-reciprocal charge transport mediated by quantum Hall states in devices composed of the intrinsic topological insulator Sn-Bi1.1Sb0.9Te2S, which is attributed to asymmetric scattering between quantum Hall states and Dirac surface states. A giant non-reciprocal coefficient of up to 2.26 × 105 A-1 is found. Our work not only reveals the properties of non-reciprocal charge transport of quantum Hall states in topological insulators but also paves the way for future electronic devices.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

Recent Advances in Broadband Photodetectors from Infrared to Terahertz

The growing need for the multiband photodetection of a single scene has promoted the development of both multispectral coupling and broadband detection technologies. Photodetectors operating across the infrared (IR) to terahertz (THz) regions have many applications such as in optical communications, sensing imaging, material identification, and biomedical detection. In this review, we present a comprehensive overview of the latest advances in broadband photodetectors operating in the infrared to terahertz range, highlighting their classification, operating principles, and performance characteristics. We discuss the challenges faced in achieving broadband detection and summarize various strategies employed to extend the spectral response of photodetectors. Lastly, we conclude by outlining future research directions in the field of broadband photodetection, including the utilization of novel materials, artificial microstructure, and integration schemes to overcome current limitations. These innovative methodologies have the potential to achieve high-performance, ultra-broadband photodetectors.

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.

Nonlinear Hall Effect from Long-Lived Valley-Polarizing Relaxons

The nonlinear Hall effect has attracted much attention due to the famous, widely adopted interpretation in terms of the Berry curvature dipole in momentum space. Using ab initio Boltzmann transport equations, we find a 60% enhancement in the nonlinear Hall effect of n-doped GeTe and its noticeable frequency dependence, qualitatively different from the predictions based on the Berry curvature dipole. The origin of these differences is long-lived valley polarization in the electron distribution arising from electron-phonon scattering. Our findings await immediate experimental confirmation.

Giant Third-Order Nonlinear Hall Effect in Misfit Layer Compound (SnS)1.17(NbS2)3

The nonlinear Hall effect (NLHE) holds immense significance in recognizing the band geometry and its potential applications in current rectification. Recent discoveries have expanded the study from second-order to third-order nonlinear Hall effect (THE), which is governed by an intrinsic band geometric quantity called the Berry Connection Polarizability tensor. Here we demonstrate a giant THE in a misfit layer compound, (SnS)1.17(NbS2)3. While the THE is prohibited in individual NbS2 and SnS due to the constraints imposed by the crystal symmetry and their band structures, a remarkable THE emerges when a superlattice is formed by introducing a monolayer of SnS. The angular-dependent THE and its scaling relationship indicate that the phenomenon could be correlated to the band geometry modulation, concurrently with the symmetry breaking. The resulting strength of THE is orders of magnitude higher compared to recent studies. Our work illuminates the modulation of structural and electronic geometries for novel quantum phenomena through interface engineering.

Odd Nonlinear Conductivity under Spatial Inversion in Chiral Tellurium

Electrical transport in noncentrosymmetric materials departs from the well-established phenomenological Ohm's law. Instead of a linear relation between current and electric field, a nonlinear conductivity emerges along specific crystallographic directions. This nonlinear transport is fundamentally related to the lack of spatial inversion symmetry. However, the experimental implications of an inversion symmetry operation on the nonlinear conductivity remain to be explored. Here, we report on a large, nonlinear conductivity in chiral tellurium. By measuring samples with opposite handedness, we demonstrate that the nonlinear transport is odd under spatial inversion. Furthermore, by applying an electrostatic gate, we modulate the nonlinear output by a factor of 300, reaching the highest reported value excluding engineered heterostructures. Our results establish chiral tellurium as an ideal compound not just to study the fundamental interplay between crystal structure, symmetry operations and nonlinear transport; but also to develop wireless rectifiers and energy-harvesting chiral devices.

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect and nonreciprocal magnetoresistance (longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in films of the doped antiferromagnetic topological insulator MnBi_{2}Te_{4}. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

Nonlinear transport and radio frequency rectification in BiTeBr at room temperature

Materials showing second-order nonlinear transport under time reversal symmetry can be used for Radio Frequency (RF) rectification, but practical application demands room temperature operation and sensitivity to microwatts level RF signals in the ambient. In this study, we demonstrate that BiTeBr exhibits a giant nonlinear response which persists up to 350 K. Through scaling and symmetry analysis, we show that skew scattering is the dominant mechanism. Additionally, the sign of the nonlinear response can be electrically switched by tuning the Fermi energy. Theoretical analysis suggests that the large Rashba spin-orbit interactions (SOI), which gives rise to the chirality of the Bloch electrons, provide the microscopic origin of the observed nonlinear response. Our BiTeBr rectifier is capable of rectifying radiation within the frequency range of 0.2 to 6 gigahertz at room temperature, even at extremely low power levels of -15 dBm, and without the need for external biasing. Our work highlights that materials exhibiting large Rashba SOI have the potential to exhibit nonlinear responses at room temperature, making them promising candidates for harvesting high-frequency and low-power ambient electromagnetic energy.

Large Nonlinear Transverse Conductivity and Berry Curvature in KTaO3 Based Two-Dimensional Electron Gas

Two-dimensional electron gas (2DEG) at oxide interfaces exhibits various exotic properties stemming from interfacial inversion and symmetry breaking. In this work, we report large nonlinear transverse conductivities in the LaAlO3/KTaO3 interface 2DEG under zero magnetic field. Skew scattering was identified as the dominant origin based on the cubic scaling of nonlinear transverse conductivity with linear longitudinal conductivity and 3-fold symmetry. Moreover, gate-tunable nonlinear transport with pronounced peak and dip was observed and reproduced by our theoretical calculation. These results indicate the presence of Berry curvature hotspots and thus a large Berry curvature triplet at the oxide interface. Our theoretical calculations confirm the existence of large Berry curvatures from the avoided crossing of multiple 5d-orbit bands, orders of magnitude larger than that in transition-metal dichalcogenides. Nonlinear transport offers a new pathway to probe the Berry curvature at oxide interfaces and facilitates new applications in oxide nonlinear electronics.

IrGe4: A Predicted Weyl-Metal with a Chiral Crystal Structure

Polycrystalline IrGe4 was synthesized by annealing elements at 800 °C for 240 h, and the composition was confirmed by energy-dispersive X-ray spectroscopy. IrGe4 adopts a chiral crystal structure (space group P3121) instead of a polar crystal structure (P31), which was corroborated by the convergent-beam electron diffraction and Rietveld refinements using synchrotron powder X-ray diffraction data. The crystal structure features layers of IrGe8 polyhedra along the b axis, and the layers are connected by edge- and corner-sharing. Each layer consists of corner-shared [Ir3Ge20] trimers, which are formed by three IrGe8 polyhedra connected by edge-sharing. Temperature-dependent resistivity indicates metallic behavior. The magnetoresistance increases with increasing applied magnetic field, and the nonsaturating magnetoresistance reaches 11.5% at 9 T and 10 K. The Hall resistivity suggests that holes are the majority carrier type, with a carrier concentration of 4.02 × 1021 cm-3 at 300 K. Electronic band structures calculated by density functional theory reveal a Weyl point with a chiral charge of +3 above the Fermi level.

Room temperature field-free switching of perpendicular magnetization through spin-orbit torque originating from low-symmetry type II Weyl semimetal

Spin-orbit torque (SOT) is a promising strategy to deterministically switch the perpendicular magnetization, but usually requires an in-plane magnetic field for breaking the mirror symmetry, which is not suitable for most advanced industrial applications. Van der Waals (vdW) materials with low crystalline symmetry and topological band structures, e.g., Weyl semimetals (WSMs), potentially serve as an outstanding system that may simultaneously realize field-free switching and high energy efficiency. Yet, the demonstration of these superiorities at room temperature has not been realized. Here, we achieve a field-free switching of perpendicular magnetization by using a layered type II WSM, TaIrTe4, in a TaIrTe4/Ti/CoFeB system at room temperature with the critical switching current density ~2.4 × 106 A cm-2. The field-free switching is ascribed to the out-of-plane SOT allowed by the low crystal symmetry. Our work suggests that using low-symmetry materials to generate SOT is a promising route for the manipulation of perpendicular magnetization at room temperature.

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.

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.

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.

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.

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.

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.

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.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

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.

Strain modulation of photocurrent in Weyl semimetal TaIrTe4

We study the effect of the strain on the energy bands of a TaIrTe₄ sheet and the photocurrent in the Cu-TaIrTe₄-Cu heterojunction by using the quantum transport simulations. It is found that the Weyl points can be completely broken with an increase of the strain along the z direction. One can obtain a large photocurrent in the Cu-TaIrTe₄-Cu heterojunction in the absence of the strain; while the photocurrent can be sharply enhanced by the strain and reach a large value. Accordingly, the maximum values of the photocurrent can be explained in terms of the transitions between peaks of density of states and band structures. The strain-induced energy bands and photocurrent exhibit anisotropic behaviors. Our results provide a novel, to the best of our knkowledge, route to effectively modulate the energy bands and the photocurrent by utilizing mechanical methods for TaIrTe₄-based 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.

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.

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.

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.

Observation of possible nonlinear anomalous Hall effect in organic two-dimensional Dirac fermion system

We report the observation of nonlinear anomalous Hall effect (NLAHE) in the multilayered organic conductor α-(BEDT-TTF)₂I₃in the charge order (CO) insulating phase just under the critical pressure for transition into two-dimensional (2D) massless Dirac fermion (DF) phase. We successfully extracted the finite nonlinear Hall voltage proportional to square current at zero magnetic field. The observed NLAHE features, current direction dependence and correlation with CO, are consistent with the previous estimation assuming 2D massive DF with a pair of tilted Dirac cones. This is the first observation of topological transport in organic conductors, and also the first example of NLAHE in the electronic phase with spontaneous symmetry breaking.

Nonlinear nanoelectrodynamics of a Weyl metal

Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe₄ As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their "symmetry fingerprints" in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe₄ single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

Rabi Regime of Current Rectification in Solids

We investigate rectified currents in response to oscillating electric fields in systems lacking inversion and time-reversal symmetries. These currents, in second-order perturbation theory, are inversely proportional to the relaxation rate, and, therefore, naively diverge in the ideal clean limit. Employing a combination of the nonequilibrium Green function technique and Floquet theory, we show that this is an artifact of perturbation theory, and that there is a well-defined periodic steady state akin to Rabi oscillations leading to finite rectified currents in the limit of weak coupling to a thermal bath. In this Rabi regime the rectified current scales as the square root of the radiation intensity, in contrast with the linear scaling of the perturbative regime, allowing us to readily diagnose it in experiments. More generally, our description provides a smooth interpolation from the ideal periodic Gibbs ensemble describing the Rabi oscillations of a closed system to the perturbative regime of rapid relaxation due to strong coupling to a thermal bath.

Quantum theory of the nonlinear Hall effect

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups C3, C3h, C3v, D3h, D3 in 2D, and T, Td, C3h, D3h in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

Layered van der Waals Topological Metals of TaTMTe4 (TM = Ir, Rh, Ru) Family

Layered van der Waals materials of the family TaTMTe₄ (TM = Ir, Rh, Ru) are showing interesting electronic properties. We report the growth and characterization of TaIrTe₄, TaRhTe₄, TaIr_1-xRh_xTe₄ (x = 0.06, 0.14, 0.78, 0.92), Ta_1+xRu_1-xTe₄ single crystals. X-ray powder diffraction confirms that TaRhTe₄ is isostructural to TaIrTe₄. All these compounds are metallic with diamagnetic behavior. Below T ≈ 4 K we observed signatures of the superconductivity in the TaIr_1-xRh_xTe₄ compounds for x = 0.92. All samples show weak quadratic-in-field magnetoresistance (MR). However, for TaIr_1-xRh_xTe₄ with x ≈ 0.78, the MR has a linear term dominating in low fields that indicates the presence of Dirac cones in the vicinity of the Fermi energy. For TaRhTe₄ series the MR is almost isotropic. Electronic structure calculations for TaIrTe₄ and TaRhTe₄ reveal appearance of the Rh band close to the Fermi level.

Multielement 2D layered material photodetectors

The pronounced quantum confinement effects, outstanding mechanical strength, strong light-matter interactions and reasonably high electric transport properties under atomically thin limit have conjointly established 2D layered materials (2DLMs) as compelling building blocks towards the next generation optoelectronic devices. By virtue of the diverse compositions and crystal structures which bring about abundant physical properties, multielement 2DLMs (ME2DLMs) have become a bran-new research focus of tremendous scientific enthusiasm. Herein, for the first time, this review provides a comprehensive overview on the latest evolution of ME2DLM photodetectors. The crystal structures, synthesis, and physical properties of various experimentally realized ME2DLMs as well as the development in metal-semiconductor-metal photodetectors are comprehensively summarized by dividing them into narrow-bandgap ME2DLMs (including Bi₂O₂X (X = S, Se, Te), EuMTe₃(M = Bi, Sb), Nb₂XTe₄(X = Si, Ge), Ta₂NiX₅(X = S, Se), M₂PdX₆(M = Ta, Nb; X = S, Se), PbSnS₂), moderate-bandgap ME2DLMs (including CuIn₇Se₁₁, CuTaS₃, GaGeTe, TlMX₂(M = Ga, In; X = S, Se)), wide-bandgap ME2DLMs (including BiOX (X = F, Cl, Br, I), MPX₃(M = Fe, Ni, Mn, Cd, Zn; X = S, Se), ABP₂X₆(A = Cu, Ag; B = In, Bi; X = S, Se), Ga₂In₄S₉), as well as topological ME2DLMs (MIrTe₄(M = Ta, Nb)). In the last section, the ongoing challenges standing in the way of further development are underscored and the potential strategies settling them are proposed, which is aimed at navigating the future advancement of this fascinating domain.

Terahertz detection based on nonlinear Hall effect without magnetic field

We propose a method for broadband long-wavelength photodetection using the nonlinear Hall effect in noncentrosymmetric quantum materials. The inherently quadratic relation between transverse current and input voltage at zero magnetic field is used to rectify the incident terahertz or infrared electric field into a direct current, without invoking any diode. Our photodetector operates at zero external bias with fast response speed and has zero threshold voltage. Remarkably, the intrinsic current responsivity due to the Berry curvature mechanism is a material property independent of the incident frequency or the scattering rate, which can be evaluated from first-principles electronic structure calculations. We identify the Weyl semimetal NbP and ferroelectric semiconductor GeTe for terahertz/infrared photodetection with large current responsivity without external bias.