Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2

The progress in exploiting new electronic materials has been a major driving force in solid-state physics. As a new state of matter, a Weyl semimetal (WSM), in particular a type-II WSM, hosts Weyl fermions as emergent quasiparticles and may harbour novel electrical transport properties. Nevertheless, such a type-II WSM material has not been experimentally observed. In this work, by performing systematic magneto-transport studies on thin films of a predicted material candidate WTe2, we observe notable negative longitudinal magnetoresistance, which can be attributed to the chiral anomaly in WSM. This phenomenon also exhibits strong planar orientation dependence with the absence along the tungsten chains, consistent with the distinctive feature of a type-II WSM. By applying a gate voltage, we demonstrate that the Fermi energy can be in-situ tuned through the Weyl points via the electric field effect. Our results may open opportunities for implementing new electronic applications, such as field-effect chiral devices.

Thermoelectric signature of the chiral anomaly in Cd3As2

Discovery of Weyl semimetals has revived interest in Weyl fermions which has not been observed in high energy experiments. It now becomes possible to study, in solids, their exotic properties. Extensive photoemission spectroscopy and electrical resistivity experiments have been carried out. However, many other properties remain unexplored. Here we show the thermoelectric signature of the chiral anomaly of Weyl fermions in Cd₃As₂ under a magnetic field. We observe a strong quadratic suppression of the thermopower when the magnetic field is parallel to the temperature gradient. The quadratic coefficient is nearly twice of that for the electrical conductivity. The thermopower reverses its sign in high fields. We show that all these intriguing observations can be understood in terms of the chiral anomaly of Weyl fermions. Our results reveal the anomalous thermoelectric property of Weyl fermions and provide insight into the chiral anomaly.

The thermoelectric effect can be used to explore electronic properties. Here, the authors show experimentally that Cd₃As₂ exhibits a negative magnetic thermopower which reverses sign at high field, and relate it to the chiral anomaly, a signature of Weyl fermions.

Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest type of single Weyl nodes with a topological charge of 1 is difficult, then making a real crystal carrying higher topological charges may seem more challenging. Here we design, and fabricate using planar fabrication technology, a photonic crystal possessing single Weyl points (including type-II nodes) and multiple Weyl points with topological charges of 2 and 3. We characterize this photonic crystal and find nontrivial 2D bulk band gaps for a fixed k_z and the associated surface modes. The robustness of these surface states against k_z-preserving scattering is experimentally observed for the first time.

To realize Weyl points carrying topological charges higher than one is challenging. Here, Chen et al. report a photonic crystal possessing single and multiple Weyl points with topological charges of two and three using planar fabrication technology.

Pressure-Induced New Topological Weyl Semimetal Phase in TaAs

We report a new pressure-induced phase in TaAs with different Weyl fermions than the ambient structure with the aid of theoretical calculations, experimental transport and synchrotron structure investigations up to 53 GPa. We show that TaAs transforms from an ambient I4_{1}md phase (t-TaAs) to a high-pressure hexagonal P-6m2  (h-TaAs) phase at 14 GPa, along with changes of the electronic state from containing 24 Weyl nodes distributed at two energy levels to possessing 12 Weyl nodes at an isoenergy level, which substantially reduces the interference between the surface and bulk states. The new pressure-induced phase can be reserved upon releasing pressure to ambient condition, which allows one to study the exotic behavior of a single set of Weyl fermions, such as the interplay between surface states and other properties.

Strong Intrinsic Spin Hall Effect in the TaAs Family of Weyl Semimetals

Since their discovery, topological insulators are expected to be ideal spintronic materials owing to the spin currents carried by surface states with spin-momentum locking. However, the bulk doping problem remains an obstacle that hinders such an application. In this work, we predict that a newly discovered family of topological materials, the Weyl semimetals, exhibits a large intrinsic spin Hall effect that can be utilized to generate and detect spin currents. Our ab initio calculations reveal a large spin Hall conductivity in the TaAs family of Weyl materials. Considering the low charge conductivity of semimetals, Weyl semimetals are believed to present a larger spin Hall angle (the ratio of the spin Hall conductivity over the charge conductivity) than that of conventional spin Hall systems such as the 4d and 5d transition metals. The spin Hall effect originates intrinsically from the bulk band structure of Weyl semimetals, which exhibit a large Berry curvature and spin-orbit coupling, so the bulk carrier problem in the topological insulators is naturally avoided. Our work not only paves the way for employing Weyl semimetals in spintronics, but also proposes a new guideline for searching for the spin Hall effect in various topological materials.

Chiral Anomaly and Giant Magnetochiral Anisotropy in Noncentrosymmetric Weyl Semimetals

We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity ρ that depends on the current I and the magnetic field B as ρ=ρ_{0}(1+γI·B), and can be applied to rectifier devices controlled by B. We derive the formula for the coefficient γ in noncentrosymmetric Weyl semimetals. The obtained formula for γ shows that the magnetochiral anisotropy is strongly enhanced when the chemical potential is tuned to Weyl points, and that noncentrosymmetric Weyl semimetals such as TaAs can exhibit much larger magnetochiral anisotropy than that observed in other materials so far.

Chiral Weyl Pockets and Fermi Surface Topology of the Weyl Semimetal TaAs

Tantalum arsenide is a member of the noncentrosymmetric monopnictides, which are putative Weyl semimetals. In these materials, three-dimensional chiral massless quasiparticles, the so-called Weyl fermions, are predicted to induce novel quantum mechanical phenomena, such as the chiral anomaly and topological surface states. However, their chirality is only well defined if the Fermi level is close enough to the Weyl points that separate Fermi surface pockets of opposite chirality exist. In this Letter, we present the bulk Fermi surface topology of high quality single crystals of TaAs, as determined by angle-dependent Shubnikov-de Haas and de Haas-van Alphen measurements combined with ab initio band-structure calculations. Quantum oscillations originating from three different types of Fermi surface pockets were found in magnetization, magnetic torque, and magnetoresistance measurements performed in magnetic fields up to 14 T and temperatures down to 1.8 K. Of these Fermi pockets, two are pairs of topologically nontrivial electron pockets around the Weyl points and one is a trivial hole pocket. Unlike the other members of the noncentrosymmetric monopnictides, TaAs is the first Weyl semimetal candidate with the Fermi energy sufficiently close to both types of Weyl points to generate chiral quasiparticles at the Fermi surface.

Collective modes in multi-Weyl semimetals

We investigate collective modes in three dimensional (3D) gapless multi-Weyl semimetals with anisotropic energy band dispersions (i.e., with a positive integer J). For comparison, we also consider the gapless semimetals with the isotropic band dispersions (i.e. E ~ kJ). We calculate analytically long-wavelength plasma frequencies incorporating interband transitions and chiral properties of carriers. For both the isotropic and anisotropic cases, we find that interband transitions and chirality lead to the depolarization shift of plasma frequencies. For the isotropic parabolic band dispersion the long-wavelength plasmons do not decay via Landau damping, while for the higher-order band dispersions the long-wavelength plasmons experience damping below a critical density. For systems with the anisotropic dispersion the density dependence of the long-wavelength plasma frequency along the direction of non-linear dispersion behaves like that of the isotropic linear band model, while along the direction of linear dispersion it behaves like that of the isotropic non-linear model. Plasmons along both directions remain undamped over a broad range of densities due to the chirality induced depolarization shift. Our results provide a comprehensive picture of how band dispersion and chirality affect plasmon behaviors in 3D gapless chiral systems with the arbitrary band dispersion.

A first theoretical realization of honeycomb topological magnon insulator

It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion symmetry of the lattice is broken by introducing a next-nearest neighbour Dzyaloshinskii-Moriya (DM) interaction. Thus, the system realizes magnon edge states similar to the Haldane model for quantum anomalous Hall effect in electronic systems. However, in contrast to electronic spin current where dissipation can be very large due to Ohmic heating, noninteracting topological magnons can propagate for a long time without dissipation as magnons are uncharged particles. We observe the same magnon edge states for the XY model on the honeycomb lattice. Remarkably, in this case the model maps to interacting hardcore bosons on the honeycomb lattice. Quantum magnetic systems with nontrivial magnon edge states are called topological magnon insulators. They have been studied theoretically on the kagome lattice and recently observed experimentally on the kagome magnet Cu(1-3, bdc) with three magnon bulk bands. Our results for the honeycomb lattice suggests an experimental procedure to search for honeycomb topological magnon insulators within a class of 2D quantum magnets and ultracold atoms trapped in honeycomb optical lattices. In 3D lattices, Dirac and Weyl points were recently studied theoretically, however, the criteria that give rise to them were not well-understood. We argue that the low-energy Hamiltonian near the Weyl points should break time-reversal symmetry of the pseudo spins. Thus, recovering the same criteria in electronic systems.

Observation of unusual topological surface states in half-Heusler compounds LnPtBi (Ln=Lu, Y)

Topological quantum materials represent a new class of matter with both exotic physical phenomena and novel application potentials. Many Heusler compounds, which exhibit rich emergent properties such as unusual magnetism, superconductivity and heavy fermion behaviour, have been predicted to host non-trivial topological electronic structures. The coexistence of topological order and other unusual properties makes Heusler materials ideal platform to search for new topological quantum phases (such as quantum anomalous Hall insulator and topological superconductor). By carrying out angle-resolved photoemission spectroscopy and ab initio calculations on rare-earth half-Heusler compounds LnPtBi (Ln=Lu, Y), we directly observe the unusual topological surface states on these materials, establishing them as first members with non-trivial topological electronic structure in this class of materials. Moreover, as LnPtBi compounds are non-centrosymmetric superconductors, our discovery further highlights them as promising candidates of topological superconductors.

Heusler compounds have been predicted to host topological order with other emergent properties, which yet awaits for experimental evidence. Here, Liu et al. report a direct observation of topological surface states on half-Heusler compounds LnPtBi.

Berry phase and band structure analysis of the Weyl semimetal NbP

Weyl semimetals are often considered the 3D-analogon of graphene or topological insulators. The evaluation of quantum oscillations in these systems remains challenging because there are often multiple conduction bands. We observe de Haas-van Alphen oscillations with several frequencies in a single crystal of the Weyl semimetal niobium phosphide. For each fundamental crystal axis, we can fit the raw data to a superposition of sinusoidal functions, which enables us to calculate the characteristic parameters of all individual bulk conduction bands using Fourier transform with an analysis of the temperature and magnetic field-dependent oscillation amplitude decay. Our experimental results indicate that the band structure consists of Dirac bands with low cyclotron mass, a non-trivial Berry phase and parabolic bands with a higher effective mass and trivial Berry phase.

Z_{2} and Chiral Anomalies in Topological Dirac Semimetals

We demonstrate that topological Dirac semimetals, which possess two Dirac nodes, separated in momentum space along a rotation axis and protected by rotational symmetry, exhibit an additional quantum anomaly, distinct from the chiral anomaly. This anomaly, which we call the Z_{2} anomaly, is a consequence of the fact that the Dirac nodes in topological Dirac semimetals carry a Z_{2} topological charge. The Z_{2} anomaly refers to nonconservation of this charge in the presence of external fields due to quantum effects and has observable consequences due to its interplay with the chiral anomaly. We discuss possible implications of this for the interpretation of magnetotransport experiments on topological Dirac semimetals. We also provide a possible explanation for the magnetic field dependent angular narrowing of the negative longitudinal magnetoresistance, observed in a recent experiment on Na_{3}Bi.

Weyl magnons in breathing pyrochlore antiferromagnets

Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogues of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example, in which Weyl points can be manipulated in situ in the laboratory by applied fields. We discuss their appearance specifically in the breathing pyrochlore lattice, and give some general discussion of conditions to find Weyl magnons, and how they may be probed experimentally. Our work may inspire a re-examination of the magnetic excitations in many magnetically ordered systems.

It was recently demonstrated that particular materials with non-trivial electronic band structure support quasiparticle excitations described by the relativistic Weyl equation. Here, the authors explore how an analogous magnonic band structure may exist in breathing pyrochlore antiferromagnets.

Weyl semimetals in optical lattices: moving and merging of Weyl points, and hidden symmetry at Weyl points

We propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points with opposite topological charges on the surface Brillouin zone is presented. By adjusting the parameters, the Weyl points can move in the Brillouin zone. Interestingly, for two pairs of Weyl points, as one pair of them meet and annihilate, the originial two Fermi arcs coneect into one. As the remaining Weyl points annihilate further, the Fermi arc vanishes and a gap is opened. Furthermore, we find that there always exists a hidden symmetry at Weyl points, regardless of anywhere they located in the Brillouin zone. The hidden symmetry has an antiunitary operator with its square being −1.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

Universal optical conductivity of a disordered Weyl semimetal

Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in the semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid. We demonstrate that the correction to the dielectric constant and optical conductivity in a dirty Weyl semimetal due to weak disorder is independent of the actual nature of point-like impurity scatterers. Therefore, optical conductivity can be used as an experimentally measurable quantity to study the critical properties and to pin the universality class of the disorder-driven quantum phase transition in Weyl semimetals.

Dirac Node Lines in Pure Alkali Earth Metals

Beryllium is a simple alkali earth metal, but has been the target of intensive studies for decades because of its unusual electron behavior at surfaces. The puzzling aspects include (i) severe deviations from the description of the nearly free-electron picture, (ii) an anomalously large electron-phonon coupling effect, and (iii) giant Friedel oscillations. The underlying origins for such anomalous surface electron behavior have been under active debate, but with no consensus. Here, by means of first-principles calculations, we discover that this pure metal system, surprisingly, harbors the Dirac node line (DNL) that in turn helps to rationalize many of the existing puzzles. The DNL is featured by a closed line consisting of linear band crossings, and its induced topological surface band agrees well with previous photoemission spectroscopy observations on the Be (0001) surface. We further reveal that each of the elemental alkali earth metals of Mg, Ca, and Sr also harbors the DNL and speculate that the fascinating topological property of the DNL might naturally exist in other elemental metals as well.

Nodal-chain metals

The band theory of solids is arguably the most successful theory of condensed-matter physics, providing a description of the electronic energy levels in various materials. Electronic wavefunctions obtained from the band theory enable a topological characterization of metals for which the electronic spectrum may host robust, topologically protected, fermionic quasiparticles. Many of these quasiparticles are analogues of the elementary particles of the Standard Model, but others do not have a counterpart in relativistic high-energy theories. A complete list of possible quasiparticles in solids is lacking, even in the non-interacting case. Here we describe the possible existence of a hitherto unrecognized type of fermionic excitation in metals. This excitation forms a nodal chain-a chain of connected loops in momentum space-along which conduction and valence bands touch. We prove that the nodal chain is topologically distinct from previously reported excitations. We discuss the symmetry requirements for the appearance of this excitation and predict that it is realized in an existing material, iridium tetrafluoride (IrF₄), as well as in other compounds of this class of materials. Using IrF₄ as an example, we provide a discussion of the topological surface states associated with the nodal chain. We argue that the presence of the nodal-chain fermions will result in anomalous magnetotransport properties, distinct from those of materials exhibiting previously known excitations.

Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals

We present a theory of thermoelectric transport in weakly disordered Weyl semimetals where the electron-electron scattering time is faster than the electron-impurity scattering time. Our hydrodynamic theory consists of relativistic fluids at each Weyl node, coupled together by perturbatively small intervalley scattering, and long-range Coulomb interactions. The conductivity matrix of our theory is Onsager reciprocal and positive semidefinite. In addition to the usual axial anomaly, we account for the effects of a distinct, axial-gravitational anomaly expected to be present in Weyl semimetals. Negative thermal magnetoresistance is a sharp, experimentally accessible signature of this axial-gravitational anomaly, even beyond the hydrodynamic limit.

Tunable Weyl Points in Periodically Driven Nodal Line Semimetals

Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measurement in film samples or by pump-probe angle-resolved photoemission spectroscopy.

Field-Selective Anomaly and Chiral Mode Reversal in Type-II Weyl Materials

Three-dimensional condensed matter incarnations of Weyl fermions generically have a tilted dispersion-in sharp contrast to their elusive high-energy relatives where a tilt is forbidden by Lorentz invariance, and with the low-energy excitations of two-dimensional graphene sheets where a tilt is forbidden by either crystalline or particle-hole symmetry. Very recently, a number of materials (MoTe_{2}, LaAlGe, and WTe_{2}) have been identified as hosts of so-called type-II Weyl fermions whose dispersion is so strongly tilted that a Fermi surface is formed, whereby the Weyl node becomes a singular point connecting electron and hole pockets. We here predict that these systems have remarkable properties in the presence of magnetic fields. Most saliently, we show that the nature of the chiral anomaly depends crucially on the relative angle between the applied field and the tilt, and that an inversion-asymmetric overtilting creates an imbalance in the number of chiral modes with positive and negative slopes. The field-selective anomaly gives a novel magneto-optical resonance, providing an experimental way to detect concealed Weyl nodes.

Magnetic-Field-Induced Relativistic Properties in Type-I and Type-II Weyl Semimetals

We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt direction. Most saliently, the tilt can be described within the relativistic framework of Lorentz transformations that give rise to a rich spectrum, displaying new transitions beyond the usual dipolar ones in the optical conductivity. We identify particular features in the latter that allow one to distinguish between semimetals of different types.

Odd Viscosity in the Quantum Critical Region of a Holographic Weyl Semimetal

We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterized by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are nonvanishing in the quantum critical region and nonzero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature. In the quantum critical region, the physics of viscosities as well as conductivities is governed by the quantum critical point.

Anomalous Phase Shift of Quantum Oscillations in 3D Topological Semimetals

Berry phase physics is closely related to a number of topological states of matter. Recently discovered topological semimetals are believed to host a nontrivial π Berry phase to induce a phase shift of ±1/8 in the quantum oscillation (+ for hole and - for electron carriers). We theoretically study the Shubnikov-de Haas oscillation of Weyl and Dirac semimetals, taking into account their topological nature and inter-Landau band scattering. For a Weyl semimetal with broken time-reversal symmetry, the phase shift is found to change nonmonotonically and go beyond known values of ±1/8 and ±5/8, as a function of the Fermi energy. For a Dirac semimetal or paramagnetic Weyl semimetal, time-reversal symmetry leads to a discrete phase shift of ±1/8 or ±5/8. Different from the previous works, we find that the topological band inversion can lead to beating patterns in the absence of Zeeman splitting. We also find the resistivity peaks should be assigned integers in the Landau index plot. Our findings may account for recent experiments in Cd_{2}As_{3} and should be helpful for exploring the Berry phase in various 3D systems.

Predicted Unusual Magnetoresponse in Type-II Weyl Semimetals

We show several distinct signatures in the magnetoresponse of type-II Weyl semimetals. The energy tilt tends to squeeze the Landau levels (LLs), and, for a type-II Weyl node, there always exists a critical angle between the B field and the tilt, at which the LL spectrum collapses, regardless of the field strength. Before the collapse, signatures also appear in the magneto-optical spectrum, including the invariable presence of intraband peaks, the absence of absorption tails, and the special anisotropic field dependence.

Photonic Weyl degeneracies in magnetized plasma

Weyl particles are elusive relativistic fermionic particles with vanishing mass. While not having been found as an elementary particle, they are found to emerge in solid-state materials where three-dimensional bands develop a topologically protected point-like crossing, a so-called Weyl point. Photonic Weyl points have been recently realised in three-dimensional photonic crystals with complex structures. Here we report the presence of a novel type of plasmonic Weyl points in a naturally existing medium-magnetized plasma, in which Weyl points arise as crossings between purely longitudinal plasma modes and transverse helical propagating modes. These photonic Weyl points are right at the critical transition between a Weyl point with the traditional closed finite equifrequency surfaces and the newly proposed 'type II' Weyl points with open equifrequency surfaces. Striking observable features of plasmon Weyl points include a half k-plane chirality manifested in electromagnetic reflection. Our study introduces Weyl physics into homogeneous photonic media, which could pave way for realizing new topological photonic devices.

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP_{2} (X=Mo, W)

The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP_{2} and WP_{2}. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the predicted topological phase robust with respect to small perturbations of the crystalline lattice. In addition, this peculiar arrangement of the Weyl points results in long topological Fermi arcs, thus making them readily accessible in angle-resolved photoemission spectroscopy.

Topological Phonons and Weyl Lines in Three Dimensions

Topological mechanics and phononics have recently emerged as an exciting field of study. Here we introduce and study generalizations of the three-dimensional pyrochlore lattice that have topologically protected edge states and Weyl lines in their bulk phonon spectra, which lead to zero surface modes that flip from one edge to the opposite as a function of surface wave number.

Topological semimetals predicted from first-principles calculations

We have given a summary on our theoretical predictions of three kinds of topological semimetals (TSMs), namely, Dirac semimetal (DSM), Weyl semimetal (WSM) and node-line semimetal (NLSM). TSMs are new states of quantum matter, which are different from topological insulators. They are characterized by the topological stability of the Fermi surface, whether it encloses band crossing points, i.e. Dirac cone-like energy nodes, or not. They are distinguished from each other by the degeneracy and momentum space distribution of the nodal points. To realize these intriguing topological quantum states is quite challenging and crucial to both fundamental science and future application. Na3Bi and Cd3As2 were theoretically predicted to be DSM in 2012 and 2013 respectively. Their experimental verification in 2014 have ignited intensive studies on TSMs. The subsequent theoretical prediction of a nonmagnetic WSM in the TaAs family stimulated a second wave and many experimental works were released out in 2015. In 2014, a kind of three dimensional crystal of carbon was proposed to be an NLSM due to negligible spin-orbit coupling and coexistence of time-reversal and inversion symmetry. Though the final experimental confirmation of NLSM is still missing, there have been several theoretical proposals, including Cu3PdN from us. In the final part, we have summarized the whole family of TSMs and their relationships.

Theoretical study of HgCr2Se3.5Te0.5: a doping-site-dependent semimetal

Weyl semimetals have recently attracted enormous attention due to their unusual features. So far, this novel state has been predicted theoretically and confirmed experimentally in several materials, such as HgTe, LaPtBi, Y₂Ir₂O₇, TaAs, TaP, NbAs, NbP and HgCr₂Se₄. Doping plays an important role in the research of condensed-matter materials. However, its influence on the Weyl semimetal has been little investigated. Here, we present detailed first-principles and theoretical studies on HgCr₂Se₄ with doping of Te atoms at the Se sites. A special case where only one pair of crossing points locates at the Fermi level is realized in HgCr₂Se_3.5Te_0.5 where one of the Se atoms in the primitive unit cell is replaced by a Te atom. A further study of k·p theory shows that the two points constitute a pair of Weyl nodes with opposite chiralities in the momentum space, and only one edge state and one single Fermi arc are obtained at each boundary of a film. Moreover, through investigations and analyses of different doping cases of HgCr₂Se_3.5Te_0.5, we find that when the type of doping induces inversion symmetry or positional disorder, the Weyl nodes transform into Dirac points resulting in a change from a Weyl semimetal to a Dirac semimetal.

Visualizing weakly bound surface Fermi arcs and their correspondence to bulk Weyl fermions

Fermi arcs are the surface manifestation of the topological nature of Weyl semimetals, enforced by the bulk-boundary correspondence with the bulk Weyl nodes. The surface of tantalum arsenide, similar to that of other members of the Weyl semimetal class, hosts nontopological bands that obscure the exploration of this correspondence. We use the spatial structure of the Fermi arc wave function, probed by scanning tunneling microscopy, as a spectroscopic tool to distinguish and characterize the surface Fermi arc bands. We find that, as opposed to nontopological states, the Fermi arc wave function is weakly affected by the surface potential: it spreads rather uniformly within the unit cell and penetrates deeper into the bulk. Fermi arcs reside predominantly on tantalum sites, from which the topological bulk bands are derived. Furthermore, we identify a correspondence between the Fermi arc dispersion and the energy and momentum of the bulk Weyl nodes that classify this material as topological. We obtain these results by introducing an analysis based on the role the Bloch wave function has in shaping quantum electronic interference patterns. It thus carries broader applicability to the study of other electronic systems and other physical processes.

MoTe_{2}: A Type-II Weyl Topological Metal

Based on the ab initio calculations, we show that MoTe_{2}, in its low-temperature orthorhombic structure characterized by an x-ray diffraction study at 100 K, realizes 4 type-II Weyl points between the Nth and (N+1)th bands, where N is the total number of valence electrons per unit cell. Other WPs and nodal lines between different other bands also appear close to the Fermi level due to a complex topological band structure. We predict a series of strain-driven topological phase transitions in this compound, opening a wide range of possible experimental realizations of different topological semimetal phases. Crucially, with no strain, the number of observable surface Fermi arcs in this material is 2-the smallest number of arcs consistent with time-reversal symmetry.

Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials

We report the existence of Weyl points in a class of noncentral symmetric metamaterials, which has time reversal symmetry, but does not have inversion symmetry due to chiral coupling between electric and magnetic fields. This class of metamaterial exhibits either type-I or type-II Weyl points depending on its nonlocal response. We also provide a physical realization of such metamaterial consisting of an array of metal wires in the shape of elliptical helices which exhibits type-II Weyl points.

Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2

Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm(2)V(-1)S(-1)) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons.

Comparative Raman study of Weyl semimetals TaAs, NbAs, TaP and NbP

We report a comparative polarized Raman study of Weyl semimetals TaAs, NbAs, TaP and NbP. The evolution of the phonon frequencies with the sample composition allows us to determine experimentally which atoms are mainly involved for each vibration mode. Our results confirm previous first-principles calculations indicating that the A1, B1(2), E(2) and E(3) modes involve mainly the As(P) atoms, the B1(1) mode is mainly related to Ta(Nb) atoms, and the E(1) mode involves both kinds of atoms. By comparing the energy of the different modes, we establish that the B1(1), B1(2), E(2) and E(3) become harder with increasing chemical pressure. This behaviour differs from our observation on the A1 mode, which decreases in energy, in contrast to its behaviour under external pressure.

Anomalous Hall Effect in a 2D Rashba Ferromagnet

Skew scattering on rare impurity configurations is shown to dominate the anomalous Hall effect in a 2D Rashba ferromagnet. The mechanism originates in scattering on rare impurity pairs separated by distances of the order of the Fermi wavelength. The corresponding theoretical description goes beyond the conventional noncrossing approximation. The mechanism provides the only contribution to the anomalous Hall conductivity in the most relevant metallic regime and strongly modifies previously obtained results for lower energies in the leading order with respect to impurity strength.

Are the surface Fermi arcs in Dirac semimetals topologically protected?

Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at [Formula: see text] where gapless states on the side surfaces are protected only near [Formula: see text] We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na3Bi and Cd3As2 Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments.

Topological boundary modes in jammed matter

Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points. The detailed statistics of the boundary modes shed surprising light on the properties of the jamming critical point and help inform a common theoretical description of the detailed features of the transition.

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review

The hot and dense matter generated in heavy-ion collisions may contain domains which are not invariant under P and CP transformations. Moreover, heavy-ion collisions can generate extremely strong magnetic fields as well as electric fields. The interplay between the electromagnetic field and triangle anomaly leads to a number of macroscopic quantum phenomena in these P- and CP-odd domains known as anomalous transports. The purpose of this article is to give a pedagogical review of various properties of the electromagnetic fields, the anomalous transport phenomena, and their experimental signatures in heavy-ion collisions.

Evidence of Topological Nodal-Line Fermions in ZrSiSe and ZrSiTe

A Dirac nodal-line semimetal phase, which represents a new quantum state of topological materials, has been experimentally realized only in a few systems, including PbTaSe_{2}, PtSn_{4}, and ZrSiS. In this Letter, we report evidence of nodal-line fermions in ZrSiSe and ZrSiTe probed in de Haas-van Alphen quantum oscillations. Although ZrSiSe and ZrSiTe share a similar layered structure with ZrSiS, our studies show the Fermi surface (FS) enclosing a Dirac nodal line has a 2D character in ZrSiTe, in contrast with 3D-like FS in ZrSiSe and ZrSiS. Another important property revealed in our experiment is that the nodal-line fermion density in this family of materials (∼10^{20}  cm^{-3}) is much higher than the Dirac fermion density of other topological materials with discrete nodes. In addition, we have demonstrated ZrSiSe and ZrSiTe single crystals can be thinned down to 2D atomic thin layers through microexfoliation, which offers the first platform to explore exotic properties of topological nodal-line fermions in low dimensions.

Magnetotransport of single crystalline YSb

We report magnetic field dependent transport measurements on a single crystal of cubic YSb together with first principles calculations of its electronic structure. The transverse magnetoresistance does not saturate up to 9 T and attains a value of 75 000% at 1.8 K. The Hall coefficient is electron-like at high temperature, changes sign to hole-like between 110 and 50 K, and again becomes electron-like below 50 K. First principles calculations show that YSb is a compensated semimetal with a qualitatively similar electronic structure to that of isostructural LaSb and LaBi, but with larger Fermi surface volume. The measured electron carrier density and Hall mobility calculated at 1.8 K, based on a single band approximation, are [Formula: see text] cm(-3) and [Formula: see text] cm(2) Vs(-1), respectively. These values are comparable with those reported for LaBi and LaSb. Like LaBi and LaSb, YSb undergoes a magnetic field-induced metal-insulator-like transition below a characteristic temperature T m, with resistivity saturation below 13 K. Thickness dependent electrical resistance measurements show a deviation of the resistance behavior from that expected for a normal metal; however, they do not unambiguously establish surface conduction as the mechanism for the resistivity plateau.

Chiral magnetic conductivity and surface states of Weyl semimetals in topological insulator ultra-thin film multilayer

We investigate an ultra-thin film of topological insulator (TI) multilayer as a model for a three-dimensional (3D) Weyl semimetal. We introduce tunneling parameters t S, [Formula: see text], and t D, where the former two parameters couple layers of the same thin film at small and large momenta, and the latter parameter couples neighbouring thin film layers along the z-direction. The Chern number is computed in each topological phase of the system and we find that for [Formula: see text], the tunneling parameter [Formula: see text] changes from positive to negative as the system transits from Weyl semi-metallic phase to insulating phases. We further study the chiral magnetic effect (CME) of the system in the presence of a time dependent magnetic field. We compute the low-temperature dependence of the chiral magnetic conductivity and show that it captures three distinct phases of the system separated by plateaus. Furthermore, we propose and study a 3D lattice model of Porphyrin thin film, an organic material known to support topological Frenkel exciton edge states. We show that this model exhibits a 3D Weyl semi-metallic phase and also supports a 2D Weyl semi-metallic phase. We further show that this model recovers that of 3D Weyl semimetal in topological insulator thin film multilayer. Thus, paving the way for simulating a 3D Weyl semimetal in topological insulator thin film multilayer. We obtain the surface states (Fermi arcs) in the 3D model and the chiral edge states in the 2D model and analyze their topological properties.

Observation of Dirac-like semi-metallic phase in NdSb

The search of new topological phases of matter is one of the new directions in condensed matter physics. Recent experimental realizations of Dirac semimetal phases pave the way to look for other exotic phases of matter in real materials. Here we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of NdSb, a potential candidate for hosting a Dirac semi-metal phase. Our studies reveal two hole-like Fermi surface pockets present at the zone center ([Formula: see text]) point as well as two elliptical electron-pockets present in the zone corner (X) point of the Brillouin zone (BZ). Interestingly, Dirac-like linearly dispersive states are observed about the zone corner (X) point in NdSb. Our first-principles calculations agree with the experimentally observed bands at the [Formula: see text] point. Moreover, the Dirac-like state observed in NdSb may be a novel correlated state, not yet predicted in calculations. Our study opens a new direction to look for Dirac semi-metal states in other members of the rare earth monopnictide family.

Phonon and thermal expansion properties in Weyl semimetals MX (M = Nb, Ta; X = P, As): ab initio studies

Weyl semimetal (WSM) is a new type of topological quantum material for future spintronic devices. Using the first-principles density functional theory, we systematically investigated the thermal expansion properties, and the temperature dependence of isovolume heat capacity and bulk modulus in WSMs MX (M = Nb, Ta; X = P, As). We also presented the phonon dispersion curves and its variation under stress in MX and the anisotropic thermal expansion properties due to the anisotropic crystal structure in WSMs have been predicted in our calculations. Intriguing, we found that the heat capacities increase more rapidly with increasing temperature in the low temperature region for all MX. Furthermore, our results showed that the thermal expansion properties are determined mainly by the isovolume heat capacity at low temperatures, while the bulk modulus has the major effect at high temperatures. These results are useful for applications of WSMs in electronic and spintronic devices.

Anomalous electronic structure and magnetoresistance in TaAs2

The change in resistance of a material in a magnetic field reflects its electronic state. In metals with weakly- or non-interacting electrons, the resistance typically increases upon the application of a magnetic field. In contrast, negative magnetoresistance may appear under some circumstances, e.g., in metals with anisotropic Fermi surfaces or with spin-disorder scattering and semimetals with Dirac or Weyl electronic structures. Here we show that the non-magnetic semimetal TaAs2 possesses a very large negative magnetoresistance, with an unknown scattering mechanism. Density functional calculations find that TaAs2 is a new topological semimetal [ℤ2 invariant (0;111)] without Dirac dispersion, demonstrating that a negative magnetoresistance in non-magnetic semimetals cannot be attributed uniquely to the Adler-Bell-Jackiw chiral anomaly of bulk Dirac/Weyl fermions.

Ideal Weyl Semimetals in the Chalcopyrites CuTlSe_{2}, AgTlTe_{2}, AuTlTe_{2}, and ZnPbAs_{2}

Weyl semimetals are new states of matter which feature novel Fermi arcs and exotic transport phenomena. Based on first-principles calculations, we report that the chalcopyrites CuTlSe_{2}, AgTlTe_{2}, AuTlTe_{2}, and ZnPbAs_{2} are ideal Weyl semimetals, having largely separated Weyl points (∼0.05  Å^{-1}) and uncovered Fermi arcs that are amenable to experimental detections. We also construct a minimal effective model to capture the low-energy physics of this class of Weyl semimetals. Our discovery is a major step toward a perfect playground of intriguing Weyl semimetals and potential applications for low-power and high-speed electronics.

A strongly robust type II Weyl fermion semimetal state in Ta3S2

Weyl semimetals are of great interest because they provide the first realization of the Weyl fermion, exhibit exotic quantum anomalies, and host Fermi arc surface states. The separation between Weyl nodes of opposite chirality gives a measure of the robustness of the Weyl semimetal state. To exploit the novel phenomena that arise from Weyl fermions in applications, it is crucially important to find robust separated Weyl nodes. We propose a methodology to design robust Weyl semimetals with well-separated Weyl nodes. Using this methodology as a guideline, we search among the material parameter space and identify by far the most robust and ideal Weyl semimetal candidate in the single-crystalline compound tantalum sulfide (Ta3S2) with new and novel properties beyond TaAs. Crucially, our results show that Ta3S2 has the largest k-space separation between Weyl nodes among known Weyl semimetal candidates, which is about twice larger than the measured value in TaAs and 20 times larger than the predicted value in WTe2. Moreover, all Weyl nodes in Ta3S2 are of type II. Therefore, Ta3S2 is a type II Weyl semimetal. Furthermore, we predict that increasing the lattice by <4% can annihilate all Weyl nodes, driving a novel topological metal-to-insulator transition from a Weyl semimetal state to a topological insulator state. The robust type II Weyl semimetal state and the topological metal-to-insulator transition in Ta3S2 are potentially useful in device applications. Our methodology can be generally applied to search for new Weyl semimetals.