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

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.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt

MnBi₂Te₄ (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi₂Te₃ phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

Intrinsic Nonlinear Hall Effect in Antiferromagnetic Tetragonal CuMnAs

Detecting the orientation of the Néel vector is a major research topic in antiferromagnetic spintronics. Here we recognize the intrinsic nonlinear Hall effect, which is independent of the relaxation time, as a prominent contribution to the time-reversal-odd second order conductivity and can be used to detect the reversal of the Néel vector. In contrast, the Berry-curvature-dipole-induced nonlinear Hall effect depends linearly on relaxation time and is time-reversal even. We study the intrinsic nonlinear Hall effect in an antiferromagnetic metal: tetragonal CuMnAs, and show that its nonlinear Hall conductivity can reach the order of mA/V^{2}. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups is presented, providing guidelines for finding more antiferromagnetic materials with the intrinsic nonlinear Hall effect.

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

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

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.

Topology and geometry under the nonlinear electromagnetic spotlight

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.

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.

Enhanced Berry Curvature Dipole and Persistent Spin Texture in the Bi(110) Monolayer

Nonvanishing Berry curvature dipole (BCD) and persistent spin texture (PST) are intriguing physical manifestations of electronic states in noncentrosymmetric 2D materials. The former induces a nonlinear Hall conductivity while the latter offers a coherent spin current. Based on density-functional-theory (DFT) calculations, we demonstrate the coexistence of both phenomena in a Bi(110) monolayer with a distorted phosphorene structure. Both effects are concurrently enhanced due to the strong spin-orbit coupling of Bi while the structural distortion creates internal in-plane ferroelectricity with inversion asymmetry. We further succeed in fabricating a Bi(110) monolayer in the desired phosphorene structure on the NbSe₂ substrate. Detailed atomic and electronic structures of the Bi(110)/NbSe₂ heterostructure are characterized by scanning tunneling microscopy/spectroscopy and angle-resolved-photoemission spectroscopy. These results are consistent with DFT calculations which indicate the large BCD and PST are retained. Our results suggest the Bi(110)/NbSe₂ heterostructure as a promising platform to exploit nonlinear Hall and coherent spin transport properties together.

Spin-Momentum Locking Induced Anisotropic Magnetoresistance in Monolayer WTe2

Monolayer WTe₂ is predicted to be a quantum spin Hall insulator (QSHI), and its quantized edge transport has recently been demonstrated. However, one of the essential properties of a QSHI, spin-momentum locking of the helical edge states, has yet to be experimentally validated. Here, we measure and observe gate-controlled anisotropic magnetoresistance (AMR) in monolayer WTe₂ devices. Electrically tuning the Fermi energy into the band gap, a large in-plane AMR is observed and the minimum of the in-plane AMR occurs when the applied magnetic field is perpendicular to the current direction. In line with the experimental observations, the theoretical predictions based on the band structure of monolayer WTe₂ demonstrate that the AMR effect originates from spin-momentum locking in the helical edge states of monolayer WTe₂. Our findings reveal that the spin quantization axis of the helical edge states in monolayer WTe₂ can be precisely determined from AMR measurements.

Noncentrosymmetric Weyl phase and topological phase transition in bulk MoTe

Ideal topological materials are those stable materials with less nontrivial band crossing near the Fermi surface and a long Fermi arc. By means of first-principles calculations, here we present that the 3D monochalcogenide molybdenum telluride (Pm-MoTe) without an inversion center shows a type-II Weyl semimetal (WSM) phase which cannot checked by symmetry index method. A total of eight Weyl points (WPs) are found in different quadrants of the Brillouin zone (BZ) of Pm-MoTe, which guarantee a long Fermi arc. The WSM phase is robust against the spin-orbit coupling (SOC) effect because of mirror symmetry and time reversal symmetry. It is also found that a topological phase transition can be tuned by strain. For different types of strain, the number of WPs can be effectively modulated to a minimum number, and their energies could be closer to Fermi level. These findings propose a promising material candidate that partly satisfies the ideal WSM criteria and extends the potential applications of the tunable topological phase.

Weyl semimetal orthorhombic Td-WTe2as an electrode material for sodium- and potassium-ion batteries

Alkali metals such as sodium and potassium have become promising candidates for the next generation of monovalent-ion batteries. However, a challenge for these battery technologies lies in the development of electrode materials that deliver high capacity and stable performance even at high cycling currents. Here we study orthorhombic tungsten ditelluride or Td-WTe₂as an electrode material for sodium- (SIB) and potassium-ion batteries (KIB) in propylene carbonate (PC) based electrolyte. Results show that despite larger Shannon's radius of potassium-ions and their sluggish diffusion in Td-WTe₂due to higher overpotential, at 100 mA.g^-1KIB-half cells showed higher cycling stability and low capacity decay of 4% versus 16% compared to SIB-half cells. Likewise, in a rate capability test at 61^stcycle (at 50 mA.g^-1), the KIB-half cells yielded charge capacity of 172 mAh.g^-1versus 137 mAh.g^-1of SIB-half cells. The superior electrochemical performance of Td-WTe₂electrode material in KIB-half cells is explained based on the concept of Stokes' radius-smaller desolvation activation energy resulted in higher mobility of potassium-ions in PC-based electrolyte. In addition, the likely mechanisms of electrochemical insertion and extraction of Na- and K-ions in Td-WTe₂are also discussed.

Terahertz response of monolayer and few-layer WTe2 at the nanoscale

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with [Formula: see text] over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit.

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.

Phonon Helicity Induced by Electronic Berry Curvature in Dirac Materials

In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over all occupied states is zero. In this Letter, we present a new effect induced by the electronic Berry curvature. By studying electron-phonon interactions in BaMnSb_{2}, a prototype two-dimensional Dirac material possessing two TR-related massive Dirac cones, we find that the nonzero local Berry curvature of electrons can induce a phonon angular momentum. The direction of this phonon angular momentum is locked to the phonon propagation direction, and thus we refer to it as "phonon helicity" in a way that is reminiscent of electron helicity in spin-orbit-coupled electronic systems. We discuss possible experimental probes of such phonon helicity.

Direct measurement of ferroelectric polarization in a tunable semimetal

Ferroelectricity, the electrostatic counterpart to ferromagnetism, has long been thought to be incompatible with metallicity due to screening of electric dipoles and external electric fields by itinerant charges. Recent measurements, however, demonstrated signatures of ferroelectric switching in the electrical conductance of bilayers and trilayers of WTe₂, a semimetallic transition metal dichalcogenide with broken inversion symmetry. An especially promising aspect of this system is that the density of electrons and holes can be continuously tuned by an external gate voltage. This degree of freedom enables measurement of the spontaneous polarization as free carriers are added to the system. Here we employ capacitive sensing in dual-gated mesoscopic devices of bilayer WTe₂ to directly measure the spontaneous polarization in the metallic state and quantify the effect of free carriers on the polarization in the conduction and valence bands, separately. We compare our results to a low-energy model for the electronic bands and identify the layer-polarized states that contribute to transport and polarization simultaneously. Bilayer WTe₂ is thus shown to be a fully tunable ferroelectric metal and an ideal platform for exploring polar ordering, ferroelectric transitions, and applications in the presence of free carriers.

Topological properties of bulk and bilayer 2M WS2: a first-principles study

Recently discovered 2M phase of bulk WS₂was observed to exhibit superconductivity with a critical temperature of 8.8 K, the highest reported among superconducting transition metal dichalcogenides. Also predicted to support protected surface states, it could be a potential topological superconductor. In the present study, we perform a detailed first-principles analysis of bulk and bilayer 2M WS₂. We report a comprehensive investigation of the bulk phase, comparing structural and electronic properties obtained from different exchange correlation functionals to the experimentally reported values. By calculation of theZ₂invariant and surface states, we give support for its non-trivial band nature. Based on the insights gained from the analysis of the bulk phase, we predict bilayer 2M WS₂as a new two-dimensional topological material. We demonstrate its dynamical stability from first-principles phonon computations and present its electronic properties, highlighting the band inversions between the Wdand Spstates. By means ofZ₂invariant computations and a calculation of the edge states, we show that bilayer 2M WS₂exhibits protected, robust edge states. The broken inversion symmetry in this newly proposed bilayer also leads to the presence of Berry curvature dipole and resulting non-linear responses. We compute the Berry curvature distribution and the dipole as a function of Fermi energy. We propose that Berry curvature dipole signals, which are absent in the centrosymmetric bulk 2M WS₂, can be signatures of the bilayer. We hope our predictions lead to the experimental realization of this as-yet-undiscovered two-dimensional topological material.

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.

Topological Phase and Quantum Anomalous Hall Effect in Ferromagnetic Transition-Metal Dichalcogenides Monolayer 1T-VSe2

Magnetic two-dimensional (2D) van der Waals materials have attracted tremendous attention because of their high potential in spintronics. In particular, the quantum anomalous Hall (QAH) effect in magnetic 2D layers shows a very promising prospect for hosting Majorana zero modes at the topologically protected edge states in proximity to superconductors. However, the QAH effect has not yet been experimentally realized in monolayer systems to date. In this work, we study the electronic structures and topological properties of the 2D ferromagnetic transition-metal dichalcogenides (TMD) monolayer 1T−VSe2 by first-principles calculations with the Heyd–Scuseria–Ernzerhof (HSE) functional. We find that the spin-orbit coupling (SOC) opens a continuous band gap at the magnetic Weyl-like crossing point hosting the quantum anomalous Hall effect with Chern number C=2. Moreover, we demonstrate the topologically protected edge states and intrinsic (spin) Hall conductivity in this magnetic 2D TMD system. Our results indicate that 1T−VSe2 monolayer serves as a stoichiometric quantum anomalous Hall material.

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

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

Infinite Berry Curvature of Weyl Fermi Arcs

We show that Weyl Fermi arcs are generically accompanied by a divergence of the surface Berry curvature scaling as 1/k^{2}, where k is the distance to a hot line in the surface Brillouin zone that connects the projection of Weyl nodes with opposite chirality, but which is distinct from the Fermi arc itself. Such surface Berry curvature appears whenever the bulk Weyl dispersion has a velocity tilt toward the surface of interest. This divergence is reflected in a variety of Berry curvature mediated effects that are readily accessible experimentally and, in particular, leads to a surface Berry curvature dipole that grows linearly with the thickness of a slab of a Weyl semimetal material in the limit of the long lifetime of surface states. This implies the emergence of a gigantic contribution to the nonlinear Hall effect in such devices.

Calculation of Berry curvature using non-orthogonal atomic orbitals

We present a derivation of the full formula to calculate the Berry curvature on non-orthogonal numerical atomic orbital (NAO) bases. Because usually, the number of NAOs is larger than that of the Wannier bases, we use a orbital contraction method to reduce the basis sizes, which can greatly improve the calculation efficiency without significantly reducing the calculation accuracy. We benchmark the formula by calculating the Berry curvature of ferroelectric BaTiO₃and bcc Fe, as well as the anomalous Hall conductivity for Fe. The results are in excellent agreement with the finite-difference and previous results in the literature. We find that there are corrections terms to the Kubo formula of the Berry curvature. For the full NAO base, the differences between the two methods are negligibly small, but for the reduced bases sets, the correction terms become larger, which may not be neglected in some cases. The formula developed in this work can readily be applied to the non-orthogonal generalized Wannier functions.

Observation of Nonlinear Spin-Charge Conversion in the Thin Film of Nominally Centrosymmetric Dirac Semimetal SrIrO_{3} at Room Temperature

Spin-charge conversion via spin-orbit interaction is one of the core concepts in the current spintronics research. The efficiency of the interconversion between charge and spin current is estimated based on Berry curvature of Bloch wave function in the linear-response regime. Beyond the linear regime, nonlinear spin-charge conversion in the higher-order electric field terms has recently been demonstrated in noncentrosymmetric materials with nontrivial spin texture in the momentum space. Here, we report the observation of the nonlinear charge-spin conversion in a nominally centrosymmetric oxide material SrIrO_{3} by breaking inversion symmetry at the interface. A large second-order magnetoelectric coefficient is observed at room temperature because of the antisymmetric spin-orbit interaction at the interface of Dirac semimetallic bands, which is subject to the symmetry constraint of the substrates. Our study suggests that nonlinear spin-charge conversion can be induced in many materials with strong spin-orbit interaction at the interface by breaking the local inversion symmetry to give rise to spin splitting in otherwise spin degenerate systems.

Correlated Magnetic Weyl Semimetal State in Strained Pr2 Ir2 O7

Correlated topological phases (CTPs) with interplay between topology and electronic correlations have attracted tremendous interest in condensed matter physics. Therein, correlated Weyl semimetals (WSMs) are rare in nature and, thus, have so far been less investigated experimentally. In particular, the experimental realization of the interacting WSM state with logarithmic Fermi velocity renormalization has not been achieved yet. Here, experimental evidence of a correlated magnetic WSM state with logarithmic renormalization in strained pyrochlore iridate Pr2 Ir2 O7 (PIO) which is a paramagnetic Luttinger semimetal in bulk, is reported. Benefitting from epitaxial strain, "bulk-absent" all-in-all-out antiferromagnetic ordering can be stabilized in PIO film, which breaks time-reversal symmetry and leads to a magnetic WSM state. With further analysis of the experimental data and renormalization group calculations, an interacting Weyl liquid state with logarithmically renormalized Fermi velocity, similar to that in graphene, is found, dressed by long-range Coulomb interactions. This work highlights the interplay of strain, magnetism, and topology with electronic correlations, and paves the way for strain-engineering of CTPs in pyrochlore iridates.

Manipulation of Stacking Order in Td-WTe2 by Ultrafast Optical Excitation

Subtle changes in stacking order of layered transition metal dichalcogenides may have profound influence on the electronic and optical properties. The intriguing electronic properties of Td-WTe2 can be traced to the break of inversion symmetry resulting from the ground-state stacking sequence. Strategies for perturbation of the stacking order are actively pursued for intentional tuning of material properties, where optical excitation is of specific interest since it holds the potential for integration of ultrafast switches in future device designs. Here we investigate the structural response in Td-WTe2 following ultrafast photoexcitation by time-resolved electron diffraction. A 0.23 THz shear phonon, involving layer displacement along the b axis, was excited by a 515 nm laser pulse. Pump fluences in excess of a threshold of ∼1 mJ/cm2 result in formation, with an ∼5 ps time constant, of a new stacking order by layer displacement along the b axis in the direction toward the centrosymmetric 1T* phase. The shear displacement of the layers increases with pump fluence until saturation at ∼8 pm. We demonstrate that the excitation of the shear phonon and the stabilization of the metastable phase are decoupled when using an optical pump as evidenced by observation of a transition also in samples with a pinned shear phonon. The results are compared to dynamic first-principles simulations and the transition is interpreted in terms of a mechanism where transient local disorder is prominent before settling at the atomic positions of the metastable phase. This interpretation is corroborated by results from diffuse scattering. The correlation between excitation of intralayer vibrations and interlayer interaction demonstrates the importance of including both short- and long-range interactions in an accurate description of how optical fields can be employed to manipulate the stacking order in 2-dimensional transition metal dichalcogenides.

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.

Giant c-axis nonlinear anomalous Hall effect in Td-MoTe2 and WTe2

While the anomalous Hall effect can manifest even without an external magnetic field, time reversal symmetry is nonetheless still broken by the internal magnetization of the sample. Recently, it has been shown that certain materials without an inversion center allow for a nonlinear type of anomalous Hall effect whilst retaining time reversal symmetry. The effect may arise from either Berry curvature or through various asymmetric scattering mechanisms. Here, we report the observation of an extremely large c-axis nonlinear anomalous Hall effect in the non-centrosymmetric Td phase of MoTe2 and WTe2 without intrinsic magnetic order. We find that the effect is dominated by skew-scattering at higher temperatures combined with another scattering process active at low temperatures. Application of higher bias yields an extremely large Hall ratio of E⊥/E|| = 2.47 and corresponding anomalous Hall conductivity of order 8 × 107 S/m.

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

The nonlinear Hall effect (NLHE), the phenomenon in which a transverse voltage can be produced without a magnetic field, provides a potential alternative for rectification or frequency doubling^1,2. However, the low-temperature detection of the NLHE limits its applications^3,4. Here, we report the room-temperature NLHE in a type-II Weyl semimetal TaIrTe₄, which hosts a robust NLHE due to broken inversion symmetry and large band overlapping at the Fermi level. We also observe a temperature-induced sign inversion of the NLHE in TaIrTe₄. Our theoretical calculations suggest that the observed sign inversion is a result of a temperature-induced shift in the chemical potential, indicating a direct correlation of the NLHE with the electronic structure at the Fermi surface. Finally, on the basis of the observed room-temperature NLHE in TaIrTe₄ we demonstrate the wireless radiofrequency (RF) rectification with zero external bias and magnetic field. This work opens a door to realizing room-temperature applications based on the NLHE in Weyl semimetals.

Colossal Terahertz Photoresponse at Room Temperature: A Signature of Type-II Dirac Fermiology

The discovery of Dirac semimetal has stimulated bourgeoning interests for exploring exotic quantum-transport phenomena, holding great promise for manipulating the performance of photoelectric devices that are related to nontrivial band topology. Nevertheless, it still remains elusive on both the device implementation and immediate results, with some enhanced or technically applicable electronic properties signified by the Dirac fermiology. By means of Pt doping, a type-II Dirac semimetal Ir_1-xPt_xTe₂ with protected crystal structure and tunable Fermi level has been achieved in this work. It has been envisioned that the metal-semimetal-metal device exhibits an order of magnitude performance improvement at terahertz frequency when the Fermi level is aligned with the Dirac node (i.e., x ∼ 0.3) and a room-temperature photoresponsivity of 0.52 A·W^-1 at 0.12 THz and 0.45 A·W^-1 at 0.3 THz, which benefited from the excitation of type-II Dirac fermions. Furthermore, van der Waals integration with Dirac semimetals exhibits superb performance with noise equivalent power less than 24 pW·Hz^-0.5, rivaling the state-of-the-art detectors. Our work provides a route to explore the nontrivial topology of Dirac semimetal for addressing targeted applications in imaging and biomedical sensing across a terahertz gap.

Momentum space toroidal moment in a photonic metamaterial

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments.

The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the “magnetic field” in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial.

Structural Phase Transition and Interlayer Coupling in Few-Layer 1T' and Td MoTe2

We performed polarized Raman spectroscopy on mechanically exfoliated few-layer MoTe₂ samples and observed both 1T' and T_d phases at room temperature. Few-layer 1T' and T_d MoTe₂ exhibited a significant difference especially in interlayer vibration modes, from which the interlayer coupling strengths were extracted using the linear chain model: strong in-plane anisotropy was observed in both phases. Furthermore, temperature-dependent Raman measurements revealed a peculiar phase transition behavior in few-layer 1T' MoTe₂. In contrast to bulk 1T' MoTe₂ crystals, where the phase transition to the T_d phase occurs at ∼250 K, the temperature-driven phase transition to the T_d phase is increasingly suppressed as the thickness is reduced, and the transition and the critical temperature varied dramatically from sample to sample even for the same thickness. Raman spectra of intermediate phases that correspond to neither 1T' nor T_d phase with different interlayer vibration modes were observed, which suggests that several metastable phases exist with similar total energies.

Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal

Nontrivial topology in condensed-matter systems enriches quantum states of matter to go beyond either the classification into metals and insulators in terms of conventional band theory or that of symmetry-broken phases by Landau's order parameter framework. So far, focus has been on weakly interacting systems, and little is known about the limit of strong electron correlations. Heavy fermion systems are a highly versatile platform to explore this regime. Here we report the discovery of a giant spontaneous Hall effect in the Kondo semimetal [Formula: see text] that is noncentrosymmetric but preserves time-reversal symmetry. We attribute this finding to Weyl nodes-singularities of the Berry curvature-that emerge in the immediate vicinity of the Fermi level due to the Kondo interaction. We stress that this phenomenon is distinct from the previously detected anomalous Hall effect in materials with broken time-reversal symmetry; instead, it manifests an extreme topological response that requires a beyond-perturbation-theory description of the previously proposed nonlinear Hall effect. The large magnitude of the effect in even tiny electric and zero magnetic fields as well as its robust bulk nature may aid the exploitation in topological quantum devices.

Quantum frequency doubling in the topological insulator Bi2Se3

The nonlinear Hall effect due to Berry curvature dipole (BCD) induces frequency doubling, which was recently observed in time-reversal-invariant materials. Here we report novel electric frequency doubling in the absence of BCD on a surface of the topological insulator Bi₂Se₃ under zero magnetic field. We observe that the frequency-doubling voltage transverse to the applied ac current shows a threefold rotational symmetry, whereas it forbids BCD. One of the mechanisms compatible with the symmetry is skew scattering, arising from the inherent chirality of the topological surface state. We introduce the Berry curvature triple, a high-order moment of the Berry curvature, to explain skew scattering under the threefold rotational symmetry. Our work paves the way to obtain a giant second-order nonlinear electric effect in high mobility quantum materials, as the skew scattering surpasses other mechanisms in the clean limit.

Berry curvature dipole (BCD) leads to the nonlinear Hall effect manifested as a frequency doubling in topological materials. Here, the authors report electric frequency doubling in the absence of BCD and magnetic field on a surface of Bi₂Se₃ due to skew scattering arising from inherent chirality of the topological surface states.

Two-Dimensional Metallic Vanadium Ditelluride as a High-Performance Electrode Material

Two-dimensional (2D) metallic transition-metal dichalcogenides (MTMDCs) are considered as ideal electrode materials for enhancing the device performances of 2D semiconducting transition-metal dichalcogenides, due to their similar atomic structures and complementary electronic properties. Vanadium ditelluride (VTe₂) behaves as a fascinating material in MTMDCs family, presenting room-temperature ferromagnetism, charge density waves order, and topological property. However, its practical applications in universal electrode/energy-related fields remain unexplored. Herein, we achieved the direct synthesis of ultrathin, large-domain, and thickness-tunable 1T-VTe₂ nanosheets on an easily available mica substrate by chemical vapor deposition (CVD). We further uncover that the CVD-derived 1T-VTe₂ can serve as a high-performance electrode material thanks to its ultrahigh conductivity. Accordingly, a 6 times higher field-effect mobility (∼47.5 cm² V^-1 s^-1) was achieved in 1T-VTe₂-contacted monolayer MoS₂ devices than that using a conventional Ti/Au electrode (∼8.1 cm² V^-1 s^-1). Moreover, the CVD-synthesized 1T-VTe₂ nanosheets are revealed to present excellent electrocatalytic activity for hydrogen evolution reaction. These results should propel the direct application of CVD-grown 2D MTMDCs as high-performance electrode materials in all 2D materials related devices.

Nonreciprocal superconducting NbSe2 antenna

The rise of two-dimensional (2D) crystalline superconductors has opened a new frontier of investigating unconventional quantum phenomena in low dimensions. However, despite the enormous advances achieved towards understanding the underlying physics, practical device applications like sensors and detectors using 2D superconductors are still lacking. Here, we demonstrate nonreciprocal antenna devices based on atomically thin NbSe₂. Reversible nonreciprocal charge transport is unveiled in 2D NbSe₂ through multi-reversal antisymmetric second harmonic magnetoresistance isotherms. Based on this nonreciprocity, our NbSe₂ antenna devices exhibit a reversible nonreciprocal sensitivity to externally alternating current (AC) electromagnetic waves, which is attributed to the vortex flow in asymmetric pinning potentials driven by the AC driving force. More importantly, a successful control of the nonreciprocal sensitivity of the antenna devices has been achieved by applying electromagnetic waves with different frequencies and amplitudes. The device’s response increases with increasing electromagnetic wave amplitude and exhibits prominent broadband sensing from 5 to 900 MHz.

Here, the authors observe reversible nonreciprocal charge transport in two-dimensional NbSe₂, and demonstrate antenna devices exhibiting strong sensitivity to driving AC electromagnetic waves in the superconducting regime.

Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states

Td-WTe₂ (non-centrosymmetric and orthorhombic), a type-II Weyl semimetal, is expected to have higher-order topological phases with topologically protected, helical one-dimensional hinge states when its Weyl points are annihilated. However, the detection of these hinge states is difficult due to the semimetallic behaviour of the bulk. In this study, we have spatially resolved the hinge states by analysing the magnetic field interference of the supercurrent in Nb-WTe₂-Nb proximity Josephson junctions. The Josephson current along the a axis of the WTe₂ crystal, but not along the b axis, showed a sharp enhancement at the edges of the junction, and the amount of enhanced Josephson current was comparable to the upper limits of a single one-dimensional helical channel. Our experimental observations suggest a higher-order topological phase in WTe₂ and its corresponding anisotropic topological hinge states, in agreement with theoretical calculations. Our work paves the way for the study of hinge states in topological transition-metal dichalcogenides and analogous phases.

Two-Dimensional Metallic NiTe2 with Ultrahigh Environmental Stability, Conductivity, and Electrocatalytic Activity

Two-dimensional (2D) metallic transition metal dichalcogenides (MTMDCs) supply a versatile platform for investigating newfangled physical issues and developing potential applications in electronics/spintronics/electrocatalysis. Among these, NiTe₂ (a type-II Dirac semimetal) possesses a Dirac point near its Fermi level. However, as-prepared 2D MTMDCs are mostly environmentally unstable, and little attention has been paid to synthesizing such materials. Herein, a general chemical vapor deposition (CVD) approach has been designed to prepare thickness-tunable and large-domain (∼1.5 mm) 1T-NiTe₂ on an atomically flat mica substrate. Significantly, ultrahigh conductivity (∼1.15 × 10⁶ S m^-1) of CVD-synthesized 1T-NiTe₂ and high catalytic activity in pH-universal hydrogen evolution reaction have been uncovered. More interestingly, the 2D 1T-NiTe₂ maintains robust environmental stability for more than one year and even after a variety of harsh treatments. These results hereby fill an existing research gap in synthesizing environmentally stable 2D MTMDCs, making fundamental progress in developing 2D MTMDC-based devices/catalysts.

Engineering Weyl Phases and Nonlinear Hall Effects in T_{d}-MoTe_{2}

MoTe_{2} has recently attracted much attention due to the observation of pressure-induced superconductivity, exotic topological phase transitions, and nonlinear quantum effects. However, there has been debate on the intriguing structural phase transitions among various observed phases of MoTe_{2} and their connection to the underlying topological electronic properties. In this work, by means of density-functional theory calculations, we investigate the structural phase transition between the polar T_{d} and nonpolar 1T^{'} phases of MoTe_{2} in reference to a hypothetical high-symmetry T_{0} phase that exhibits higher-order topological features. In the T_{d} phase we obtain a total of 12 Weyl points, which can be created/annihilated, dynamically manipulated, and switched by tuning a polar phonon mode. We also report the existence of a tunable nonlinear Hall effect in T_{d}-MoTe_{2} and propose the use of this effect as a probe for the detection of polarity orientation in polar (semi)metals. By studying the role of dimensionality, we identify a configuration in which a nonlinear surface response current emerges. The potential technological applications of the tunable Weyl phase and the nonlinear Hall effect are discussed.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Wannier90 as a community code: new features and applications

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

Anisotropic Picosecond Spin-Photocurrent from Weyl Semimetal WTe2

The generation and detection of ultrafast spin current, preferably reaching a frequency up to terahertz, is the core of spintronics. Studies have shown that the Weyl semimetal WTe₂ is of great potential in generating spin currents. However, the prior studies have been limited to the static measurements with the in-plane spin orientation. In this work, we demonstrate a picosecond spin-photocurrent in a Td-WTe₂ thin film via a terahertz time domain spectroscopy with a circularly polarized laser excitation. The anisotropic dependence of the circular photogalvanic effect (CPGE) in the terahertz emission reveals that the picosecond spin-photocurrent is generated along the rotational asymmetry a-axis. Notably, the generated spins are aligned along the out-of-plane direction under the light normally incident to the film surface, which provides an efficient means to manipulate magnetic devices with perpendicular magnetic anisotropy. A spin-splitting band induced by intrinsic inversion symmetry breaking enables the manipulation of a spin current by modulating the helicity of the laser excitation. Moreover, CPGE nearly vanishes at a transition temperature of ∼175 K due to the carrier compensation. Our work provides an insight into the dynamic behavior of the anisotropic spin-photocurrent of Td-WTe₂ in terahertz frequencies and shows a great potential for the future development of terahertz-spintronic devices with Weyl semimetals.

Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature

The spin Hall effect (SHE) is usually observed as a bulk effect in high-symmetry crystals with substantial spin-orbit coupling (SOC), where the symmetric spin-orbit field imposes a widely encountered trade-off between spin Hall angle (θ_SH) and spin diffusion length (L_sf), and spin polarization, spin current and charge current are constrained to be mutually orthogonal. Here, we report a large θ_SH of 0.32 accompanied by a long L_sf of 2.2 μm at room temperature in a low-symmetry few-layered semimetal MoTe₂, thus identifying it as an excellent candidate for simultaneous spin generation, transport and detection. In addition, we report that longitudinal spin current with out-of-plane polarization can be generated by both transverse and vertical charge current, due to the conventional and a newly observed planar SHE, respectively. Our study suggests that manipulation of crystalline symmetries and strong SOC opens access to new charge-spin interconversion configurations and spin-orbit torques for spintronic applications.