Temperature-Induced Lifshitz Transition in WTe2

Influence of Lifshitz Transition on the Intrinsic Resistivity of Cu2N Monolayer

The Lifshitz transition (LT), a topological structure transition of Fermi surfaces, can induce various intricate physical properties in metallic materials. In this study, through first-principles calculations, we explore the nontrivial effect of the LT on the intrinsic resistivity of the Cu2N monolayer arising from electron-phonon (el-ph) scattering. We find that when the LT is induced by electron doping, the multibranch Fermi surface simplifies into a single-band profile. Such an LT leads to a decoupling of low-frequency flexural phonons from el-ph scattering due to mirror symmetry. Consequently, the resistivity of the Cu2N monolayer at room temperature significantly decreases, approaching that of slightly doped graphene, and highlighting the Cu2N monolayer as a highly conductive two-dimensional metal. Moreover, this LT can bring about a nonlinear temperature dependence of the intrinsic resistivity at a high temperature.

Temperature-dependent Fermi surface probed by Shubnikov-de Haas oscillations in topological semimetal candidates DyBi and HoBi

Rare earth-based monopnictides are among the most intensively studied groups of materials in which extremely large magnetoresistance has been observed. This study explores magnetotransport properties of two representatives of this group, DyBi and HoBi. The extreme magnetoresistance is discovered in DyBi and confirmed in HoBi. At [Formula: see text] K and in [Formula: see text] T for both compounds, magnetoresistance reaches the order of magnitude of [Formula: see text]. For both materials, standard Kohler's rule is obeyed only in the temperature range from 50 to 300 K. At lower temperatures, extended Kohler's rule has to be invoked because carrier concentrations and mobilities strongly change with temperature and magnetic field. This is further proven by the observation of a quite rare temperature-dependence of oscillation frequencies in Shubnikov-de Haas effect. Rate of this dependence clearly changes at Néel temperature, reminiscent of a novel magnetic band splitting. Multi-frequency character of the observed Shubnikov-de Haas oscillations points to the coexistence of electron- and hole-type Fermi pockets in both studied materials. Overall, our results highlight correlation of temperature dependence of the Fermi surface with the magnetotransport properties of DyBi and HoBi.

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

Tunable optical topological transitions of plasmon polaritons in WTe2 van der Waals films

Naturally existing in-plane hyperbolic polaritons and the associated optical topological transitions, which avoid the nano-structuring to achieve hyperbolicity, can outperform their counterparts in artificial metasurfaces. Such plasmon polaritons are rare, but experimentally revealed recently in WTe2 van der Waals thin films. Different from phonon polaritons, hyperbolic plasmon polaritons originate from the interplay of free carrier Drude response and interband transitions, which promise good intrinsic tunability. However, tunable in-plane hyperbolic plasmon polariton and its optical topological transition of the isofrequency contours to the elliptic topology in a natural material have not been realized. Here we demonstrate the tuning of the optical topological transition through Mo doping and temperature. The optical topological transition energy is tuned over a wide range, with frequencies ranging from 429 cm-1 (23.3 microns) for pure WTe2 to 270 cm-1 (37.0 microns) at the 50% Mo-doping level at 10 K. Moreover, the temperature-induced blueshift of the optical topological transition energy is also revealed, enabling active and reversible tuning. Surprisingly, the localized surface plasmon resonance in skew ribbons shows unusual polarization dependence, accurately manifesting its topology, which renders a reliable means to track the topology with far-field techniques. Our results open an avenue for reconfigurable photonic devices capable of plasmon polariton steering, such as canaling, focusing, and routing, and pave the way for low-symmetry plasmonic nanophotonics based on anisotropic natural materials.

Experimental Realization of a Three-Dimensional Dirac Semimetal Phase with a Tunable Lifshitz Transition in Au_{2}Pb

Three-dimensional Dirac semimetals are an exotic state of matter that continue to attract increasing attention due to the unique properties of their low-energy excitations. Here, by performing angle-resolved photoemission spectroscopy, we investigate the electronic structure of Au_{2}Pb across a wide temperature range. Our experimental studies on the (111)-cleaved surface unambiguously demonstrate that Au_{2}Pb is a three-dimensional Dirac semimetal characterized by the presence of a bulk Dirac cone projected off-center of the bulk Brillouin zone (BZ), in agreement with our theoretical calculations. Unusually, we observe that the bulk Dirac cone is significantly shifted by more than 0.4 eV to higher binding energies with reducing temperature, eventually going through a Lifshitz transition. The pronounced downward shift is qualitatively reproduced by our calculations indicating that an enhanced orbital overlap upon compression of the lattice, which preserves C_{4} rotational symmetry, is the main driving mechanism for the Lifshitz transition. These findings not only broaden the range of currently known materials exhibiting three-dimensional Dirac phases, but also show a viable mechanism by which it could be possible to switch on and off the contribution of the degeneracy point to electron transport without external doping.

Gate-Tunable Multiband Transport in ZrTe5 Thin Devices

Interest in ZrTe₅ has been reinvigorated in recent years owing to its potential for hosting versatile topological electronic states and intriguing experimental discoveries. However, the mechanism of many of its unusual transport behaviors remains controversial: for example, the characteristic peak in the temperature-dependent resistivity and the anomalous Hall effect. Here, through employing a clean dry-transfer fabrication method in an inert environment, we successfully obtain high-quality ZrTe₅ thin devices that exhibit clear dual-gate tunability and ambipolar field effects. Such devices allow us to systematically study the resistance peak as well as the Hall effect at various doping densities and temperatures, revealing the contribution from electron-hole asymmetry and multiple-carrier transport. By comparing with theoretical calculations, we suggest a simplified semiclassical two-band model to explain the experimental observations. Our work helps to resolve the longstanding puzzles on ZrTe₅ and could potentially pave the way for realizing novel topological states in the two-dimensional limit.

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

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

Gate-tunable transport in van der Waals topological insulator Bi4Br4nanobelts

Bi₄Br₄is a quasi-one-dimensional van der Waals topological insulator with novel electronic properties. Several efforts have been devoted to the understanding of its bulk form, yet it remains a challenge to explore the transport properties in low-dimensional structures due to the difficulty of device fabrication. Here we report for the first time a gate-tunable transport in exfoliated Bi₄Br₄nanobelts. Notable two-frequency Shubnikov-de Haas oscillations oscillations are discovered at low temperatures, with the low- and high-frequency parts coming from the three-dimensional bulk state and the two-dimensional surface state, respectively. In addition, ambipolar field effect is realized with a longitudinal resistance peak and a sign reverse in the Hall coefficient. Our successful measurements of quantum oscillations and realization of gate-tunable transport lay a foundation for further investigation of novel topological properties and room-temperature quantum spin Hall states in Bi₄Br₄.

Superconductivity Induced by Lifshitz Transition in Pristine SnS2 under High Pressure

The importance of electronic structure evolutions and reconstitutions is widely acknowledged for strongly correlated systems. The precise effect of pressurized Fermi surface topology on metallization and superconductivity is a much-debated topic. In this work, an evolution from insulating to metallic behavior, followed by a superconducting transition, is systematically investigated in SnS₂ under high pressure. In-situ X-ray diffraction measurements show the stability of the trigonal structure under compression. Interestingly, a Lifshitz transition, which has an important bearing on the metallization and superconductivity, is identified by the first-principles calculations between 35 and 40 GPa. Our findings provide a unique playground for exploring the relationship of electronic structure, metallization, and superconductivity under high pressure without crystal structural collapse.

A two-dimensional topological nodal-line material MgN4 with extremely large magnetoresistance

Using first-principles calculations, we predict a stable two-dimensional atomically thin material MgN₄. This material has a perfect intrinsic electron-hole compensation characteristic with high carrier mobility, making it a promising candidate material with extremely large magnetoresistance. As the magnetic field increases, the magnetoresistance of the monolayer MgN₄ will show a quadratic dependence on the strength of the magnetic field without saturation. Furthermore, nontrivial topological properties are also found in this material. In the absence of spin-orbit coupling, the monolayer MgN₄ belongs to a topological nodal-line material, in which the band crossings form a closed saddle-shape nodal-ring near the Fermi level in the Brillouin zone. Once the spin-orbit coupling is considered, a small local energy gap is opened along the nodal ring, resulting in a topological insulator defined on a curved Fermi surface with ₂ = 1. The combination of two-dimensional single-atomic-layer thickness, an extremely large magnetoresistance effect, and topological non-trivial properties in the monolayer MgN₄ makes it an excellent platform for designing novel multi-functional devices.

Direct observation of vortices in an electron fluid

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance^1-4, higher-than-ballistic conduction^5-7, Poiseuille flow in narrow channels^8-10 and violation of the Wiedemann-Franz law¹¹. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip¹², we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe₂. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Large-Gap Quantum Spin Hall State and Temperature-Induced Lifshitz Transition in Bi4Br4

Searching for quantum spin Hall insulators with large fully opened energy gap to overcome the thermal disturbance at room temperature has attracted tremendous attention because of the robustness of one-dimensional (1D) spin-momentum locked topological edge states in the practical applications of electronic devices and spintronics. Here, we report the investigation of topological nature of monolayer Bi₄Br₄ by the techniques of angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy. The possible topological nontriviality of 1D edge state integrals within the large energy gap (∼0.2 eV) is revealed by the first-principle calculations. The ARPES measurements at different temperatures show a temperature-induced Lifshitz transition, corresponding to the resistivity anomaly evoked by the chemical potential shift. The connection between the emergency of superconductivity and the Lifshitz transition is discussed.

Materials and possible mechanisms of extremely large magnetoresistance: a review

Magnetoresistance (MR) is a characteristic that the resistance of a substance changes with the external magnetic field, reflecting various physical origins and microstructures of the substance. A large MR, namely a huge response to a low external field, has always been a useful functional feature in industrial technology and a core goal pursued by physicists and materials scientists. Conventional large MR materials are mainly manganites, whose colossal MR (CMR) can be as high as -90%. The dominant mechanism is attributed to spin configuration aligned by the external field, which reduces magnetic scattering and thus resistance. In recent years, some new systems have shown an extremely large unsaturated MR (XMR). Unlike ordinary metals, the positive MR of these systems can reach 10³%-10⁸% and is persistent under super high magnetic fields. The XMR materials are mainly metals or semimetals, distributed in high-mobility topological or non-topological systems, and some are magnetic, which suggests a wide range of application scenarios. Various mechanisms have been proposed for the potential physical origin of XMR, including electron-hole compensation, steep band, ultrahigh mobility, high residual resistance ratio, topological fermions, etc. It turns out that some mechanisms play a leading role in certain systems, while more are far from clearly defined. In addition, the researches on XMR are largely overlapped or closely correlated with other recently rising physics and materials researches, such as topological matters and two-dimensional (2D) materials, which makes elucidating the mechanism of XMR even more important. Moreover, the disclosed novel properties will lay a broad and solid foundation for the design and development of functional devices. In this review, we will discuss several aspects in the following order: (I) introduction, (II) XMR materials and classification, (III) proposed mechanisms for XMR, (IV) correlation with other systems (featured), and (V) conclusions and outlook.

Magnetism-induced topological transition in EuAs3

The nature of the interaction between magnetism and topology in magnetic topological semimetals remains mysterious, but may be expected to lead to a variety of novel physics. We systematically studied the magnetic semimetal EuAs3, demonstrating a magnetism-induced topological transition from a topological nodal-line semimetal in the paramagnetic or the spin-polarized state to a topological massive Dirac metal in the antiferromagnetic ground state at low temperature. The topological nature in the antiferromagnetic state and the spin-polarized state has been verified by electrical transport measurements. An unsaturated and extremely large magnetoresistance of ~2 × 105% at 1.8 K and 28.3 T is observed. In the paramagnetic states, the topological nodal-line structure at the Y point is proven by angle-resolved photoemission spectroscopy. Moreover, a temperature-induced Lifshitz transition accompanied by the emergence of a new band below 3 K is revealed. These results indicate that magnetic EuAs3 provides a rich platform to explore exotic physics arising from the interaction of magnetism with topology.

Direct Visualization of Large-Scale Intrinsic Atomic Lattice Structure and Its Collective Anisotropy in Air-Sensitive Monolayer 1T'- WTe2

Probing large-scale intrinsic structure of air-sensitive 2D materials with atomic resolution is so far challenging due to their rapid oxidization and contamination. Here, by keeping the whole experiment including growth, transfer, and characterizations in an interconnected atmosphere-control environment, the large-scale intact lattice structure of air-sensitive monolayer 1T'-WTe₂ is directly visualized by atom-resolved scanning transmission electron microscopy. Benefit from the large-scale atomic mapping, collective lattice distortions are further unveiled due to the presence of anisotropic rippling, which propagates perpendicular to only one of the preferential lattice planes in the same WTe₂ monolayer. Such anisotropic lattice rippling modulates the intrinsic point defect (Te vacancy) distribution, in which they aggregate at the constrictive inner side of the undulating structure, presumably due to the ripple-induced asymmetric strain as elaborated by density functional theory. The results pave the way for atomic characterizations and defect engineering of air-sensitive 2D layered materials.

Anisotropic Optical Response of WTe2 Single Crystals Studied by Ellipsometric Analysis

In this paper we report the crystal growth conditions and optical anisotropy properties of Tungsten ditelluride (WTe₂) single crystals. The chemical vapor transport (CVT) method was used for the synthesis of large WTe₂ crystals with high crystallinity and surface quality. These were structurally and morphologically characterized by means of X-ray diffraction, optical profilometry and Raman spectroscopy. Through spectroscopic ellipsometry analysis, based on the Tauc–Lorentz model, we identified a high refractive index value (~4) and distinct tri-axial anisotropic behavior of the optical constants, which opens prospects for surface plasmon activity, revealed by the dielectric function. The anisotropic physical nature of WTe₂ shows practical potential for low-loss light modulation at the 2D nanoscale level.

Defect induced ferromagnetic ordering and room temperature negative magnetoresistance in MoTeP

The magneto-transport, magnetization and theoretical electronic-structure have been investigated on type-II Weyl semimetallic MoTeP. The ferromagnetic ordering is observed in the studied sample and it has been shown that the observed magnetic ordering is due to the defect states. It has also been demonstrated that the presence of ferromagnetic ordering in effect suppresses the magnetoresistance (MR) significantly. Interestingly, a change-over from positive to negative MR is observed at higher temperature which has been attributed to the dominance of spin scattering suppression.

Ultrafast dynamical Lifshitz transition

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal T _d-MoTe₂ We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

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.

Lifshitz Transition and Non-Fermi Liquid Behavior in Highly Doped Semimetals

The classical Fermi liquid theory and Drude model have provided fundamental ways to understand the resistivity of most metals. The violation of the classical theory, known as non-Fermi liquid (NFL) transport, appears in certain metals, including topological semimetals, but quantitative understanding of the NFL behavior has not yet been established. In particular, the determination of the non-quadratic temperature exponent in the resistivity, a sign of NFL behavior, remains a puzzling issue. Here, a physical model to quantitatively explain the Lifshitz transition and NFL behavior in highly doped (a carrier density of ≈10²² cm^-3 ) monoclinic Nb₂ Se₃ is reported. Hall and magnetoresistance measurements, the two-band Drude model, and first-principles calculations demonstrate an apparent chemical potential shift by temperature in monoclinic Nb₂ Se₃ , which induces a Lifshitz transition and NFL behavior in the material. Accordingly, the non-quadratic temperature exponent in the resistivity can be quantitatively determined by the chemical potential shift under the framework of Fermi liquid theory. This model provides a new experimental insight for nontrivial transport with NFL behavior or sign inversion of Seebeck coefficients in emerging materials.

Temperature-Induced Lifshitz Transition and Possible Excitonic Instability in ZrSiSe

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy (spectroscopy) [STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a V-shaped dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures.

A combined laser-based angle-resolved photoemission spectroscopy and two-photon photoemission spectroscopy study ofTd-WTe2

Laser-based angle-resolved photoemission spectroscopy and two-photon photoemission spectroscopy are employed to study the valence electronic structure of the Weyl semimetal candidateTd-WTe2along two high symmetry directions and for binding energies between ≈ -1 eV and 5 eV. The experimental data show a good agreement with band structure calculations. Polarization dependent measurements provide further information on initial and intermediate state symmetry properties with respect to the mirror plane of theTdstructure of WTe2.

Magnetoelastoresistance in WTe2: Exploring electronic structure and extremely large magnetoresistance under strain

Strain describes the deformation of a material as a result of applied stress. It has been widely employed to probe transport properties of materials, ranging from semiconductors to correlated materials. In order to understand, and eventually control, transport behavior under strain, it is important to quantify the effects of strain on the electronic bandstructure, carrier density, and mobility. Here, we demonstrate that much information can be obtained by exploring magnetoelastoresistance (MER), which refers to magnetic field-driven changes of the elastoresistance. We use this powerful approach to study the combined effect of strain and magnetic fields on the semimetallic transition metal dichalcogenide [Formula: see text] We discover that WTe₂ shows a large and temperature-nonmonotonic elastoresistance, driven by uniaxial stress, that can be tuned by magnetic field. Using first-principle and analytical low-energy model calculations, we provide a semiquantitative understanding of our experimental observations. We show that in [Formula: see text], the strain-induced change of the carrier density dominates the observed elastoresistance. In addition, the change of the mobilities can be directly accessed by using MER. Our analysis also reveals the importance of a heavy-hole band near the Fermi level on the elastoresistance at intermediate temperatures. Systematic understanding of strain effects in single crystals of correlated materials is important for future applications, such as strain tuning of bulk phases and fabrication of devices controlled by strain.

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe_{2} (X=Mo,W)

In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials. In particular, monolayers of centrosymmetric β-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric γ-phase MoTe_{2} and WTe_{2} have been identified as type-II Weyl semimetals. However, angle-resolved photoemission spectroscopy and STM probes of these semimetals have revealed huge, arclike surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this Letter, we calculate the bulk and surface electronic structure of both β- and γ-MoTe_{2}. We find that β-MoTe_{2} is, in fact, a Z_{4}-nontrivial higher-order TI (HOTI) driven by double band inversion and exhibits the same surface features as γ-MoTe_{2} and γ-WTe_{2}. We discover that these surface states are not topologically trivial, as previously characterized by the research that differentiated them from the Weyl Fermi arcs but, rather, are the characteristic split and gapped fourfold Dirac surface states of a HOTI. In β-MoTe_{2}, this indicates that it would exhibit helical pairs of hinge states if it were bulk insulating, and in γ-MoTe_{2} and γ-WTe_{2}, these surface states represent vestiges of HOTI phases without inversion symmetry that are nearby in parameter space. Using nested Wilson loops and first-principles calculations, we explicitly demonstrate that, when the Weyl points in γ-MoTe_{2} are annihilated, which may be accomplished by symmetry-preserving strain or lattice distortion, γ-MoTe_{2} becomes a nonsymmetry-indicated, noncentrosymmetric HOTI. We also show that, when the effects of spin-orbit coupling are neglected, β-MoTe_{2} is a nodal-line semimetal with Z_{2}-nontrivial monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by double band inversion are the weak-spin-orbit coupling limit of HOTIs, implying that MNLSMs are higher-order topological semimetals with flat-band-like hinge states, which we find to originate from the corner modes of 2D "fragile" TIs.

Remarkable electronic and optical anisotropy of layered 1T'-WTe2 2D materials

Anisotropic 2D materials exhibit novel optical, electrical and thermoelectric properties that open possibilities for a great variety of angle-dependent devices. Recently, quantitative research on 1T'-WTe₂ has been reported, revealing its fascinating physical properties such as non-saturating magnetoresistance, highly anisotropic crystalline structure and anisotropic optical/electrical response. Especially for its anisotropic properties, surging research interest devoted solely to understanding its structural and optical properties has been undertaken. Here we report quantitative, comprehensive work on the highly anisotropic, optical, electrical and optoelectronic properties of few-layer 1T'-WTe₂ by azimuth-dependent reflectance difference microscopy, DC conductance measurements, as well as polarization-resolved and wavelength-dependent optoelectrical measurements. The electrical conductance anisotropic ratio is found to ≈10³ for a thin 1T'-WTe₂ film, while the optoelectronic anisotropic ratio is around 300 for this material. The polarization dependence of the photo-response is ascribed to the unique anisotropic in-plane crystal structure, consistent with the optical absorption anisotropy results. In general, 1T'-WTe₂, with its highly anisotropic electrical and photoresponsivity reported here, demonstrates a route to exploit the intrinsic anisotropy of 2D materials and the possibility to open up new ways for applications of 2D materials for light polarization detection.

Direct Evidence for Charge Compensation-Induced Large Magnetoresistance in Thin WTe2

Since the discovery of extremely large nonsaturating magnetoresistance (MR) in WTe₂, much effort has been devoted to understanding the underlying mechanism, which is still under debate. Here, we explicitly identify the dominant physical origin of the large nonsaturating MR through in situ tuning of the magneto-transport properties in thin WTe₂ film. With an electrostatic doping approach, we observed a nonmonotonic gate dependence of the MR. The MR reaches a maximum (10600%) in thin WTe₂ film at certain gate voltage where electron and hole concentrations are balanced, indicating that the charge compensation is the dominant mechanism of the observed large MR. Besides, we show that the temperature-dependent magnetoresistance exhibits similar tendency with the carrier mobility when the charge compensation is retained, revealing that distinct scattering mechanisms may be at play for the temperature dependence of magneto-transport properties. Our work would be helpful for understanding mechanism of the large MR in other nonmagnetic materials and offers an avenue for achieving large MR in the nonmagnetic materials with electron-hole pockets.

Charge Disproportionation Triggers Bipolar Doping in FeSb2- xSn xSe4 Ferromagnetic Semiconductors, Enabling a Temperature-Induced Lifshitz Transition

Ferromagnetic semiconductors (FMSs) featuring a high Curie transition temperature ( T_c) and a strong correlation between itinerant carriers and localized magnetic moments are of tremendous importance for the development of practical spintronic devices. The realization of such materials hinges on the ability to generate and manipulate a high density of itinerant spin-polarized carriers and the understanding of their responses to external stimuli. In this study, we demonstrate the ability to tune magnetic ordering in the p-type FMS FeSb_{2- x}Sn _xSe₄ (0 ≤ x ≤ 0.20) through carrier density engineering. We found that the substitution of Sb by Sn FeSb_{2- x}Sn _xSe₄ increases the ordering of metal atoms within the selenium crystal lattice, leading to a large separation between magnetic centers. This results in a decrease in the T_c from 450 K for samples with x ≤ 0.05 to 325 K for samples with 0.05 < x ≤ 0.2. In addition, charge disproportionation arising from the substitution of Sb³⁺ by Sn²⁺ triggers the partial oxidation of Sb³⁺ to Sb⁵⁺, which is accompanied by the generation of both electrons and holes. This leads to a drastic decrease in the electrical resistivity and thermopower simultaneously with a large increase in the magnetic susceptibility and saturation magnetization upon increasing Sn content. The observed bipolar doping induces a very interesting temperature-induced quantum electronic transition (Lifshitz transition), which is manifested by the presence of an anomalous peak in the resistivity curve simultaneously with a reversal of the sign of a majority of the charge carriers from hole-like to electron-like at the temperature of maximum resistivity. This study suggests that while there is a strong correlation between the overall magnetic moment and free carrier spin in FeSb_{2- x}Sn _xSe₄ FMSs, the magnitude of the Curie temperature strongly depends on the spatial separation between localized magnetic centers rather than the concentration of magnetic atoms or the density of itinerant carriers.

Anomalous Photothermoelectric Transport Due to Anisotropic Energy Dispersion in WTe2

Band structures are vital in determining the electronic properties of materials. Recently, the two-dimensional (2D) semimetallic transition metal tellurides (WTe₂ and MoTe₂) have sparked broad research interest because of their elliptical or open Fermi surface, making distinct from the conventional 2D materials. In this study, we demonstrate a centrosymmetric photothermoelectric voltage distribution in WTe₂ nanoflakes, which has not been observed in common 2D materials such as graphene and MoS₂. Our theoretical model shows the anomalous photothermoelectric effect arises from an anisotropic energy dispersion and micrometer-scale hot carrier diffusion length of WTe₂. Further, our results are more consistent with the anisotropic tilt direction of energy dispersion being aligned to the b-axis rather than the a-axis of the WTe₂ crystal, which is consistent with the previous first-principle calculations as well as magneto-transport experiments. Our work shows the photothermoelectric current is strongly confined to the anisotropic direction of the energy dispersion in WTe₂, which opens an avenue for interesting electro-optic applications such as electron beam collimation and electron lenses.

Nonlinear magnetotransport shaped by Fermi surface topology and convexity

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe₂, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe₂, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

Thermopower and Unconventional Nernst Effect in the Predicted Type-II Weyl Semimetal WTe2

WTe₂ is one of a series of recently discovered high mobility semimetals, some of whose properties are characteristic of topological Dirac or Weyl metals. One of its most interesting properties is the unsaturated giant magnetoresistance that it exhibits at low temperatures. An important question is the degree to which this property can be ascribed to a conventional semimetallic model in which a highly compensated, high mobility metal exhibits large magnetoresistance. Here, we show that the longitudinal thermopower (Seebeck effect) of semimetallic WTe₂ exfoliated flakes exhibits periodic sign changes about zero with increasing magnetic field that indicates distinct electron and hole Landau levels and nearly fully compensated electron and hole carrier densities. However, inconsistent with a conventional semimetallic picture, we find a rapid enhancement of the Nernst effect at low temperatures that is nonlinear in magnetic field, which is consistent with Weyl points in proximity to the Fermi energy. Hence, we demonstrate the role played by the Weyl character of WTe₂ in its transport properties.

Origin of extremely large magnetoresistance in the candidate type-II Weyl semimetal MoTe2-x

The recent observation of extremely large magnetoresistance (MR) in the transition-metal dichalcogenide MoTe₂ has attracted considerable interest due to its potential technological applications as well as its relationship with novel electronic states predicted for a candidate type-II Weyl semimetal. In order to understand the origin of the MR, the electronic structure of MoTe_2−x (x = 0.08) is systematically tuned by application of pressure and probed via its Hall and longitudinal conductivities. With increasing pressure, a monoclinic-to-orthorhombic (1 T′ to T_d) structural phase transition temperature (T*) gradually decreases from 210 K at 1 bar to 58 K at 1.1 GPa, and there is no anomaly associated with the phase transition at 1.4 GPa, indicating that a T = 0 K quantum phase transition occurs at a critical pressure (P_c) between 1.1 and 1.4 GPa. The large MR observed at 1 bar is suppressed with increasing pressure and is almost saturated at 100% for P > P_c. The dependence on magnetic field of the Hall and longitudinal conductivities of MoTe_2−x shows that a pair of electron and hole bands are important in the low-pressure T_d phase, while another pair of electron and hole bands are additionally required in the high-pressure 1 T′ phase. The MR peaks at a characteristic hole-to-electron concentration ratio (n_c) and is sharply suppressed when the ratio deviates from n_c within the T_d phase. These results establish the comprehensive temperature-pressure phase diagram of MoTe_2−x and underscore that its MR originates from balanced electron-hole carrier concentrations.

Tunable Lifshitz Transitions and Multiband Transport in Tetralayer Graphene

As the Fermi level and band structure of two-dimensional materials are readily tunable, they constitute an ideal platform for exploring the Lifshitz transition, a change in the topology of a material's Fermi surface. Using tetralayer graphene that host two intersecting massive Dirac bands, we demonstrate multiple Lifshitz transitions and multiband transport, which manifest as a nonmonotonic dependence of conductivity on the charge density n and out-of-plane electric field D, anomalous quantum Hall sequences and Landau level crossings that evolve with n, D, and B.

Magnetoresistance and robust resistivity plateau in MoAs2

We have grown the MoAs2 single crystal which crystallizes in a monoclinic structure with C2/m space group. Transport measurements show that MoAs2 displays a metallic behavior at zero field and undergoes a metal-to-semiconductor crossover at low temperatures when the applied magnetic field is over 5 T. A robust resistivity plateau appears below 18 K and persists for the field up to 9 T. A large positive magnetoresistance (MR), reaching about 2600% at 2 K and 9 T, is observed when the field is perpendicular to the current. The MR becomes negative below 40 K when the field is rotated to be parallel to the current. The Hall resistivity shows the non-linear field-dependence below 70 K. The analysis using two-band model indicates a compensated electron-hole carrier density at low temperatures. A combination of the breakdown of Kohler's rule, the abnormal drop and the cross point in Hall data implies that a possible Lifshitz transition has occurred between 30 K and 60 K, likely driving the compensated electron-hole density, the large MR as well as the metal-semiconductor transition in MoAs2. Our results indicate that the family of centrosymmetric transition-metal dipnictides has rich transport behavior which can in general exhibit variable metallic and topological features.

Three-Dimensional Electronic Structure of the Type-II Weyl Semimetal WTe_{2}

By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of WTe_{2}, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the Γ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe_{2} around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5

The topological materials have attracted much attention for their unique electronic structure and peculiar physical properties. ZrTe₅ has host a long-standing puzzle on its anomalous transport properties manifested by its unusual resistivity peak and the reversal of the charge carrier type. It is also predicted that single-layer ZrTe₅ is a two-dimensional topological insulator and there is possibly a topological phase transition in bulk ZrTe₅. Here we report high-resolution laser-based angle-resolved photoemission measurements on the electronic structure and its detailed temperature evolution of ZrTe₅. Our results provide direct electronic evidence on the temperature-induced Lifshitz transition, which gives a natural understanding on underlying origin of the resistivity anomaly in ZrTe₅. In addition, we observe one-dimensional-like electronic features from the edges of the cracked ZrTe₅ samples. Our observations indicate that ZrTe₅ is a weak topological insulator and it exhibits a tendency to become a strong topological insulator when the layer distance is reduced.

To understand the anomalous electronic transport properties of ZrTe₅ remains an elusive puzzle. Here, Zhang et al. report direct electronic evidence to the origin of the resistivity anomaly and temperature induced Lifshitz transition in ZrTe₅, indicating it being a weak topological insulator.

Magnetoresistance and Hall resistivity of semimetal WTe2 ultrathin flakes

This article reports the characterization of WTe₂ thin flake magnetoresistance and Hall resistivity. We found it does not exhibit magnetoresistance saturation when subject to high fields, in a manner similar to their bulk characteristics. The linearity of Hall resistivity in our devices confirms the compensation of electrons and holes. By relating experimental results to a classic two-band model, the lower magnetoresistance values in our samples is demonstrated to be caused by decreased carrier mobility. The dependence of mobility on temperature indicates the main role of optical phonon scattering at high temperatures. Our results provide more detailed information on carrier behavior and scattering mechanisms in WTe₂ thin films.

Angle-resolved photoemission spectroscopy for the study of two-dimensional materials

Quantum systems in confined geometries allow novel physical properties that cannot easily be attained in their bulk form. These properties are governed by the changes in the band structure and the lattice symmetry, and most pronounced in their single layer limit. Angle-resolved photoemission spectroscopy (ARPES) is a direct tool to investigate the underlying changes of band structure to provide essential information for understanding and controlling such properties. In this review, recent progresses in ARPES as a tool to study two-dimensional atomic crystals have been presented. ARPES results from few-layer and bulk crystals of material class often referred as “beyond graphene” are discussed along with the relevant developments in the instrumentation.

Distinct Electronic Structure for the Extreme Magnetoresistance in YSb

An extreme magnetoresistance (XMR) has recently been observed in several nonmagnetic semimetals. Increasing experimental and theoretical evidence indicates that the XMR can be driven by either topological protection or electron-hole compensation. Here, by investigating the electronic structure of a XMR material, YSb, we present spectroscopic evidence for a special case which lacks topological protection and perfect electron-hole compensation. Further investigations reveal that a cooperative action of a substantial difference between electron and hole mobility and a moderate carrier compensation might contribute to the XMR in YSb.

Giant magnetoresistance, three-dimensional Fermi surface and origin of resistivity plateau in YSb semimetal

Very strong magnetoresistance and a resistivity plateau impeding low temperature divergence due to insulating bulk are hallmarks of topological insulators and are also present in topological semimetals where the plateau is induced by magnetic field, when time-reversal symmetry (protecting surface states in topological insulators) is broken. Similar features were observed in a simple rock-salt-structure LaSb, leading to a suggestion of the possible non-trivial topology of 2D states in this compound. We show that its sister compound YSb is also characterized by giant magnetoresistance exceeding one thousand percent and low-temperature plateau of resistivity. We thus performed in-depth analysis of YSb Fermi surface by band calculations, magnetoresistance, and Shubnikov–de Haas effect measurements, which reveals only three-dimensional Fermi sheets. Kohler scaling applied to magnetoresistance data accounts very well for its low-temperature upturn behavior. The field-angle-dependent magnetoresistance demonstrates a 3D-scaling yielding effective mass anisotropy perfectly agreeing with electronic structure and quantum oscillations analysis, thus providing further support for 3D-Fermi surface scenario of magnetotransport, without necessity of invoking topologically non-trivial 2D states. We discuss data implying that analogous field-induced properties of LaSb can also be well understood in the framework of 3D multiband model.

Tuning the magnetoresistance of ultrathin WTe2 sheets by electrostatic gating

The semimetallic, two-dimensional layered transition metal dichalcogenide WTe₂ has raised considerable interest due to its huge, non-saturating magnetoresistance. While for the origin of this effect, a close-to-ideal balance of electrons and holes has been put forward, the carrier concentration dependence of the magnetoresistance remains to be clarified. Here, we present a detailed study of the magnetotransport behaviour of ultrathin, mechanically exfoliated WTe₂ sheets as a function of electrostatic back gating. The carrier concentration and mobility, determined using the two band model and analysis of the Shubnikov-de Haas oscillations, indicate enhanced surface scattering for the thinnest sheets. By the back gate action, the magnetoresistance could be tuned by up to ∼100% for a ∼13 nm-thick WTe₂ sheet.

Direct Observation of a Long-Range Field Effect from Gate Tuning of Nonlocal Conductivity

We report the direct observation of a long-range field effect in WTe_{2} devices, leading to large gate-induced changes of transport through crystals much thicker than the electrostatic screening length. The phenomenon-which manifests itself very differently from the conventional field effect-originates from the nonlocal nature of transport in the devices that are thinner than the carrier mean free path. We reproduce theoretically the gate dependence of the measured classical and quantum magnetotransport, and show that the phenomenon is caused by the gate tuning of the bulk carrier mobility by changing the scattering at the surface. Our results demonstrate experimentally the possibility to gate tune the electronic properties deep in the interior of conducting materials, avoiding limitations imposed by electrostatic screening.

Compensated Semimetal LaSb with Unsaturated Magnetoresistance

By combining angle-resolved photoemission spectroscopy and quantum oscillation measurements, we performed a comprehensive investigation on the electronic structure of LaSb, which exhibits near-quadratic extremely large magnetoresistance (XMR) without any sign of saturation at magnetic fields as high as 40 T. We clearly resolve one spherical and one intersecting-ellipsoidal hole Fermi surfaces (FSs) at the Brillouin zone (BZ) center Γ and one ellipsoidal electron FS at the BZ boundary X. The hole and electron carriers calculated from the enclosed FS volumes are perfectly compensated, and the carrier compensation is unaffected by temperature. We further reveal that LaSb is topologically trivial but shares many similarities with the Weyl semimetal TaAs family in the bulk electronic structure. Based on these results, we have examined the mechanisms that have been proposed so far to explain the near-quadratic XMR in semimetals.

Thermally Driven Electronic Topological Transition in FeTi

Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M_{5}^{-} phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoes a novel thermally driven electronic topological transition, in which new features of the Fermi surface arise at elevated temperatures. The thermally induced electronic topological transition causes an increased electronic screening for the atom displacements in the M_{5}^{-} phonon mode and an adiabatic electron-phonon interaction with an unusual temperature dependence.

Coherent optical phonon oscillation and possible electronic softening in WTe2 crystals

A rapidly-growing interest in WTe2 has been triggered by the giant magnetoresistance effect discovered in this unique system. While many efforts have been made towards uncovering the electron- and spin-relevant mechanisms, the role of lattice vibration remains poorly understood. Here, we study the coherent vibrational dynamics in WTe2 crystals by using ultrafast pump-probe spectroscopy. The oscillation signal in time domain in WTe2 has been ascribed as due to the coherent dynamics of the lowest energy A1 optical phonons with polarization- and wavelength-dependent measurements. With increasing temperature, the phonon energy decreases due to anharmonic decay of the optical phonons into acoustic phonons. Moreover, a significant drop (15%) of the phonon energy with increasing pump power is observed which is possibly caused by the lattice anharmonicity induced by electronic excitation and phonon-phonon interaction.

Layer-dependent quantum cooperation of electron and hole states in the anomalous semimetal WTe2

The behaviour of electrons and holes in a crystal lattice is a fundamental quantum phenomenon, accounting for a rich variety of material properties. Boosted by the remarkable electronic and physical properties of two-dimensional materials such as graphene and topological insulators, transition metal dichalcogenides have recently received renewed attention. In this context, the anomalous bulk properties of semimetallic WTe₂ have attracted considerable interest. Here we report angle- and spin-resolved photoemission spectroscopy of WTe₂ single crystals, through which we disentangle the role of W and Te atoms in the formation of the band structure and identify the interplay of charge, spin and orbital degrees of freedom. Supported by first-principles calculations and high-resolution surface topography, we reveal the existence of a layer-dependent behaviour. The balance of electron and hole states is found only when considering at least three Te–W–Te layers, showing that the behaviour of WTe₂ is not strictly two dimensional.

Tungsten ditelluride is a semi-metallic two-dimensional material that has exhibited large magnetoresistance. Here, the authors use angle- and spin-resolved photoemission spectroscopy to investigate the band structure of this transition metal dichalcogenide and identify layer-dependent electronic behaviour.

Prediction of an arc-tunable Weyl Fermion metallic state in Mo(x)W(1-x)Te2

A Weyl semimetal is a new state of matter that hosts Weyl fermions as emergent quasiparticles. The Weyl fermions correspond to isolated points of bulk band degeneracy, Weyl nodes, which are connected only through the crystal's boundary by exotic Fermi arcs. The length of the Fermi arc gives a measure of the topological strength, because the only way to destroy the Weyl nodes is to annihilate them in pairs in the reciprocal space. To date, Weyl semimetals are only realized in the TaAs class. Here, we propose a tunable Weyl state in Mo(x)W(1-x)Te2 where Weyl nodes are formed by touching points between metallic pockets. We show that the Fermi arc length can be changed as a function of Mo concentration, thus tuning the topological strength. Our results provide an experimentally feasible route to realizing Weyl physics in the layered compound Mo(x)W(1-x)Te2, where non-saturating magneto-resistance and pressure-driven superconductivity have been observed.

The polarization-dependent anisotropic Raman response of few-layer and bulk WTe2under different excitation wavelengths

WTe₂, which is an orthorhombic semimetal crystallized in Td phase, exhibts distinct in-plane anisotropy. The Raman modes depict different anisotropic response by rotating the incident polarization under different excitation wavelengths.

Ultrafast Optical Control of the Electronic Properties of ZrTe₅

We report on the temperature dependence of the ZrTe(5) electronic properties, studied at equilibrium and out of equilibrium, by means of time and angle resolved photoelectron spectroscopy. Our results unveil the dependence of the electronic band structure across the Fermi energy on the sample temperature. This finding is regarded as the dominant mechanism responsible for the anomalous resistivity observed at T*∼160  K along with the change of the charge carrier character from holelike to electronlike. Having addressed these long-lasting questions, we prove the possibility to control, at the ultrashort time scale, both the binding energy and the quasiparticle lifetime of the valence band. These experimental evidences pave the way for optically controlling the thermoelectric and magnetoelectric transport properties of ZrTe(5).

Signature of Strong Spin-Orbital Coupling in the Large Nonsaturating Magnetoresistance Material WTe2

We report the detailed electronic structure of WTe2 by high resolution angle-resolved photoemission spectroscopy. We resolved a rather complicated Fermi surface of WTe2. Specifically, there are in total nine Fermi pockets, including one hole pocket at the Brillouin zone center Γ, and two hole pockets and two electron pockets on each side of Γ along the Γ-X direction. Remarkably, we have observed circular dichroism in our photoemission spectra, which suggests that the orbital angular momentum exhibits a rich texture at various sections of the Fermi surface. This is further confirmed by our density-functional-theory calculations, where the spin texture is qualitatively reproduced as the conjugate consequence of spin-orbital coupling. Since the spin texture would forbid backscatterings that are directly involved in the resistivity, our data suggest that the spin-orbit coupling and the related spin and orbital angular momentum textures may play an important role in the anomalously large magnetoresistance of WTe2. Furthermore, the large differences among spin textures calculated for magnetic fields along the in-plane and out-of-plane directions also provide a natural explanation of the large field-direction dependence on the magnetoresistance.