Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena

Superconductivity Provides Access to the Chiral Magnetic Effect of an Unpaired Weyl Cone

The massless fermions of a Weyl semimetal come in two species of opposite chirality, in two cones of the band structure. As a consequence, the current j induced in one Weyl cone by a magnetic field B [the chiral magnetic effect (CME)] is canceled in equilibrium by an opposite current in the other cone. Here, we show that superconductivity offers a way to avoid this cancellation, by means of a flux bias that gaps out a Weyl cone jointly with its particle-hole conjugate. The remaining gapless Weyl cone and its particle-hole conjugate represent a single fermionic species, with renormalized charge e^{*} and a single chirality ± set by the sign of the flux bias. As a consequence, the CME is no longer canceled in equilibrium but appears as a supercurrent response ∂j/∂B=±(e^{*}e/h^{2})μ along the magnetic field at chemical potential μ.

Numerical Study of Nonperturbative Corrections to the Chiral Separation Effect in Quenched Finite-Density QCD

We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

Anomalous Nernst Effect in the Dirac Semimetal Cd_{3}As_{2}

Dirac and Weyl semimetals display a host of novel properties. In Cd_{3}As_{2}, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in a zero magnetic field, resulting in ultrahigh mobility (∼10^{7}  cm^{2} V^{-1} s^{-1}). In an applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report the observation of a large anomalous Nernst effect in Cd_{3}As_{2}. Both the anomalous Nernst signal and transport relaxation time τ_{tr} begin to increase rapidly at ∼50  K. This suggests a close relation between the protection mechanism and the anomalous Nernst effect. In a field, the quantum oscillations of bulk states display a beating effect, suggesting that the Dirac nodes split into Weyl states, allowing the Berry curvature to be observed as an anomalous Nernst effect.

Dynamic Chiral Magnetic Effect and Faraday Rotation in Macroscopically Disordered Helical Metals

We develop an effective medium theory for electromagnetic wave propagation through gapless nonuniform systems with a dynamic chiral magnetic effect. The theory allows us to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of the optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. The absolute value of the effect varies strongly depending on the system parameters, but yields the leading frequency dependence of the polarization rotation and circular dichroism signals. Experimentally, these corrections can be observed as features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonances of a material. Such features are not expected to be present in single-crystal samples.

Experimental Observation of Anisotropic Adler-Bell-Jackiw Anomaly in Type-II Weyl Semimetal WTe_{1.98} Crystals at the Quasiclassical Regime

The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here, we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted WTe_{1.98} crystals. Quantitatively, C_{W}, a coefficient representing the intensity of the ABJ anomaly along the a and b axis of WTe_{1.98} are 0.030 and 0.051  T^{-2} at 2 K, respectively. We found that the temperature-sensitive ABJ anomaly is attributed to a topological phase transition from a type-II Weyl semimetal to a trivial semimetal, which is verified by a first-principles calculation using experimentally determined lattice parameters at different temperatures. Theoretical electrical transport study reveals that the observation of an anisotropic ABJ along both the a and b axes in WTe_{1.98} is attributed to electrical transport in the quasiclassical regime. Our work may suggest that electron-doped WTe_{2} is an ideal playground to explore the novel properties in type-II Weyl semimetals.

Switching of a large anomalous Hall effect between metamagnetic phases of a non-collinear antiferromagnet

The anomalous Hall effect (AHE), which in long-range ordered ferromagnets appears as a voltage transverse to the current and usually is proportional to the magnetization, often is believed to be of negligible size in antiferromagnets due to their low uniform magnetization. However, recent experiments and theory have demonstrated that certain antiferromagnets with a non-collinear arrangement of magnetic moments exhibit a sizeable spontaneous AHE at zero field due to a non-vanishing Berry curvature arising from the quantum mechanical phase of the electron’s wave functions. Here we show that antiferromagnetic Mn₅Si₃ single crystals exibit a large AHE which is strongly anisotropic and shows multiple transitions with sign changes at different magnetic fields due to field-induced rearrangements of the magnetic structure despite only tiny variations of the total magnetization. The presence of multiple non-collinear magnetic phases offers the unique possiblity to explore the details of the AHE and the sensitivity of the Hall effect on the details of the magnetic texture.

Tunable Positive to Negative Magnetoresistance in Atomically Thin WTe2

Transitional metal ditelluride WTe₂ has been extensively studied owing to its intriguing physical properties like nonsaturating positive magnetoresistance and being possibly a type-II Weyl semimetal. While surging research activities were devoted to the understanding of its bulk properties, it remains a substantial challenge to explore the pristine physics in atomically thin WTe₂. Here, we report a successful synthesis of mono- to few-layer WTe₂ via chemical vapor deposition. Using atomically thin WTe₂ nanosheets, we discover a previously inaccessible ambipolar behavior that enables the tunability of magnetoconductance of few-layer WTe₂ from weak antilocalization to weak localization, revealing a strong electrical field modulation of the spin-orbit interaction under perpendicular magnetic field. These appealing physical properties unveiled in this study clearly identify WTe₂ as a promising platform for exotic electronic and spintronic device applications.

Room-temperature chiral charge pumping in Dirac semimetals

Chiral anomaly, a non-conservation of chiral charge pumped by the topological nontrivial gauge fields, has been predicted to exist in Weyl semimetals. However, until now, the experimental signature of this effect exclusively relies on the observation of negative longitudinal magnetoresistance at low temperatures. Here, we report the field-modulated chiral charge pumping process and valley diffusion in Cd₃As₂. Apart from the conventional negative magnetoresistance, we observe an unusual nonlocal response with negative field dependence up to room temperature, originating from the diffusion of valley polarization. Furthermore, a large magneto-optic Kerr effect generated by parallel electric and magnetic fields is detected. These new experimental approaches provide a quantitative analysis of the chiral anomaly phenomenon which was inaccessible previously. The ability to manipulate the valley polarization in topological semimetal at room temperature opens up a route towards understanding its fundamental properties and utilizing the chiral fermions.

Magnetotransport signature of topological semimetal states has been observed but restricted at very low temperature. Here, Zhang et al. report magnetic field-modulated chiral charge pumping and valley diffusion in Cd₃As₂ up to room temperature.

Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe5 single crystal

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.

Three-dimensional Majorana fermions in chiral superconductors

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Electromagnetic Signatures of the Chiral Anomaly in Weyl Semimetals

Weyl semimetals are predicted to realize the three-dimensional axial anomaly first discussed in particle physics. The anomaly leads to unusual transport phenomena such as the chiral magnetic effect in which an applied magnetic field induces a current parallel to the field. Here we investigate diagnostics of the axial anomaly based on the fundamental equations of axion electrodynamics. We find that materials with Weyl nodes of opposite chirality and finite energy separation immersed in a uniform magnetic field exhibit an anomaly-induced oscillatory magnetic field with a period set by the chemical potential difference of the nodes. In the case where a chemical potential imbalance is created by applying parallel electric and magnetic fields, we find a suppression of the magnetic-field component parallel to the electric field inside the material for rectangular samples, suggesting that the chiral magnetic current opposes this imbalance. For cylindrical geometries, we instead find an enhancement of this magnetic-field component along with an anomaly-induced azimuthal component. We propose experiments to detect such magnetic signatures of the axial anomaly.

Surface to bulk Fermi arcs via Weyl nodes as topological defects

A hallmark of Weyl semimetal is the existence of surface Fermi arcs. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal-to-surface direction is . The Zak phase can reveal the peculiar topological structure of Weyl semimetal directly in the bulk. Here, we show that the winding of the Zak phase around each projected Weyl node manifests itself as a topological defect of the Wannier–Stark ladder, energy eigenstates under an electric field. Remarkably, this leads to bulk Fermi arcs, open-line segments in the bulk spectra. Bulk Fermi arcs should exist in conjunction with surface counterparts to conserve the Weyl fermion number under an electric field, which is supported by explicit numerical evidence.

Understanding how surface Fermi arcs connect different Weyl nodes in presence of multiple Weyl-node pairs is intriguing yet unclear. Here, Kim et al. show that the winding of the Zak phase around each projected Weyl node manifests itself as a topological defect, leading to non-trivial surface as well as bulk Fermi arcs.

Quantum Oscillations at Integer and Fractional Landau Level Indices in Single-Crystalline ZrTe5

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. 3D DSs have been a fertile playground in discovering novel quantum particles, for example Weyl fermions, in solid state systems. Many 3D DSs were theoretically predicted and experimentally confirmed. We report here the results in exfoliated ZrTe₅ thin flakes from the studies of aberration-corrected scanning transmission electron microscopy and low temperature magneto-transport measurements. Several unique results were observed. First, a π Berry phase was obtained from the Landau fan diagram of the Shubnikov-de Haas oscillations in the longitudinal conductivity σ_xx. Second, the longitudinal resistivity ρ_xx shows a linear magnetic field dependence in the quantum limit regime. Most surprisingly, quantum oscillations were also observed at fractional Landau level indices N = 5/3 and 7/5, demonstrating strong electron-electron interaction effects in ZrTe₅.

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.

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.

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.

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.

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.

Two-Carrier Transport Induced Hall Anomaly and Large Tunable Magnetoresistance in Dirac Semimetal Cd3As2 Nanoplates

Cd3As2 is a model material of Dirac semimetal with a linear dispersion relation along all three directions in the momentum space. The unique band structure of Cd3As2 is made with both Dirac and topological properties. It can be driven into a Weyl semimetal by symmetry breaking or a topological insulator by enhancing the spin-orbit coupling. Here we report the temperature and gate voltage-dependent magnetotransport properties of Cd3As2 nanoplates with Fermi level near the Dirac point. The Hall anomaly demonstrates the two-carrier transport accompanied by a transition from n-type to p-type conduction with decreasing temperature. The carrier-type transition is explained by considering the temperature-dependent spin-orbit coupling. The magnetoresistance exhibits a large nonsaturating value up to 2000% at high temperatures, which is ascribed to the electron-hole compensation in the system. Our results are valuable for understanding the experimental observations related to the two-carrier transport in Dirac/Weyl semimetals, such as Na3Bi, ZrTe5, TaAs, NbAs, and HfTe5.

Large transverse Hall-like signal in topological Dirac semimetal Cd3As2

Cadmium arsenide (Cd₃As₂) is known for its inverted band structure and ultra-high electron mobility. It has been theoretically predicted and also confirmed by ARPES experiments to exhibit a 3D Dirac semimetal phase containing degenerate Weyl nodes. From magneto-transport measurements in high quality single crystals of Cd₃As₂, a small effective mass m^* ≈ 0.05 m_e is determined from the Shubnikov-de Haas (SdH) oscillations. In certain field orientations, we find a splitting of the SdH oscillation frequency in the FFT spectrum suggesting a possible lifting of the double degeneracy in accord with the helical spin texture at outer and inner Fermi surfaces with opposite chirality predicted by our ab initio calculations. Strikingly, a large antisymmetric magnetoresistance with respect to the applied magnetic fields is uncovered over a wide temperature range in needle crystal of Cd₃As₂ with its long axis along [112] crystal direction. It reveals a possible contribution of intrinsic anomalous velocity term in the transport equation resulting from a unique 3D Rashba-like spin splitted bands that can be obtained from band calculations with the inclusion of Cd antisite defects.

Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP

Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands disperse linearly around pairs of nodes with fixed chirality, the Weyl points. In WSMs, nonorthogonal electric and magnetic fields induce an exotic phenomenon known as the chiral anomaly, resulting in an unconventional negative longitudinal magnetoresistance, the chiral-magnetic effect. However, it remains an open question to which extent this effect survives when chirality is not well-defined. Here, we establish the detailed Fermi-surface topology of the recently identified WSM TaP via combined angle-resolved quantum-oscillation spectra and band-structure calculations. The Fermi surface forms banana-shaped electron and hole pockets surrounding pairs of Weyl points. Although this means that chirality is ill-defined in TaP, we observe a large negative longitudinal magnetoresistance. We show that the magnetoresistance can be affected by a magnetic field-induced inhomogeneous current distribution inside the sample.

Torsional Chiral Magnetic Effect in a Weyl Semimetal with a Topological Defect

We propose a torsional response raised by a lattice dislocation in Weyl semimetals akin to a chiral magnetic effect; i.e., a fictitious magnetic field arising from a screw or edge dislocation induces a charge current. We demonstrate that, in sharp contrast to the usual chiral magnetic effect that vanishes in real solid state materials, the torsional chiral magnetic effect exists even for realistic lattice models, which implies the experimental detection of the effect via superconducting quantum interference device or nonlocal resistivity measurements in Weyl semimetal materials.

Interplanar coupling-dependent magnetoresistivity in high-purity layered metals

The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here we report a hitherto unobserved magnetoresistive effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the interlayer coupling disappearing for fields applied along the so-called Yamaji angles where the interlayer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral (for example, Weyl) fermions. Its observation in PdCoO₂, PtCoO₂ and Sr₂RuO₄ suggests that the anomaly affects the transport of clean conductors, in particular near the quantum limit.

In Weyl semimetals, unusual electronic transport phenomena are predicted to occur, such as an axial anomaly which violates the conservation of chiral fermions. Here, the authors evidence such behaviour via the occurrence of negative magnetoresistance in layered high-purity non-magnetic metals.

Weak antilocalization in Cd3As2 thin films

Recently, it has been theoretically predicted that Cd3As2 is a three dimensional Dirac material, a new topological phase discovered after topological insulators, which exhibits a linear energy dispersion in the bulk with massless Dirac fermions. Here, we report on the low-temperature magnetoresistance measurements on a ~50 nm-thick Cd3As2 film. The weak antilocalization under perpendicular magnetic field is discussed based on the two-dimensional Hikami-Larkin-Nagaoka (HLN) theory. The electron-electron interaction is addressed as the source of the dephasing based on the temperature-dependent scaling behavior. The weak antilocalization can be also observed while the magnetic field is parallel to the electric field due to the strong interaction between the different conductance channels in this quasi-two-dimensional film.

Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal

Weyl semimetals provide the realization of Weyl fermions in solid-state physics. Among all the physical phenomena that are enabled by Weyl semimetals, the chiral anomaly is the most unusual one. Here, we report signatures of the chiral anomaly in the magneto-transport measurements on the first Weyl semimetal TaAs. We show negative magnetoresistance under parallel electric and magnetic fields, that is, unlike most metals whose resistivity increases under an external magnetic field, we observe that our high mobility TaAs samples become more conductive as a magnetic field is applied along the direction of the current for certain ranges of the field strength. We present systematically detailed data and careful analyses, which allow us to exclude other possible origins of the observed negative magnetoresistance. Our transport data, corroborated by photoemission measurements, first-principles calculations and theoretical analyses, collectively demonstrate signatures of the Weyl fermion chiral anomaly in the magneto-transport of TaAs.

Negative magnetoresistance in Dirac semimetal Cd3As2

A large negative magnetoresistance (NMR) is anticipated in topological semimetals in parallel magnetic fields, demonstrating the chiral anomaly, a long-sought high-energy-physics effect, in solid-state systems. Recent experiments reveal that the Dirac semimetal Cd3As2 has the record-high mobility and positive linear magnetoresistance in perpendicular magnetic fields. However, the NMR has not yet been unveiled. Here we report the observation of NMR in Cd3As2 microribbons in parallel magnetic fields up to 66% at 50 K and visible at room temperatures. The NMR is sensitive to the angle between magnetic and electrical fields, robust against temperature and dependent on the carrier density. The large NMR results from low carrier densities in our Cd3As2 samples, ranging from 3.0 × 10(17) cm(-3) at 300 K to 2.2 × 10(16) cm(-3) below 50 K. We therefore attribute the observed NMR to the chiral anomaly. In perpendicular magnetic fields, a positive linear magnetoresistance up to 1,670% at 14 T and 2 K is also observed.

π Berry phase and Zeeman splitting of Weyl semimetal TaP

The recent breakthrough in the discovery of Weyl fermions in monopnictide semimetals provides opportunities to explore the exotic properties of relativistic fermions in condensed matter. The chiral anomaly-induced negative magnetoresistance and π Berry phase are two fundamental transport properties associated with the topological characteristics of Weyl semimetals. Since monopnictide semimetals are multiple-band systems, resolving clear Berry phase for each Fermi pocket remains a challenge. Here we report the determination of Berry phases of multiple Fermi pockets of Weyl semimetal TaP through high field quantum transport measurements. We show our TaP single crystal has the signatures of a Weyl state, including light effective quasiparticle masses, ultrahigh carrier mobility, as well as negative longitudinal magnetoresistance. Furthermore, we have generalized the Lifshitz-Kosevich formula for multiple-band Shubnikov-de Haas (SdH) oscillations and extracted the Berry phases of π for multiple Fermi pockets in TaP through the direct fits of the modified LK formula to the SdH oscillations. In high fields, we also probed signatures of Zeeman splitting, from which the Landé g-factor is extracted.

Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires

Dirac electronic materials beyond graphene and topological insulators have recently attracted considerable attention. Cd3As2 is a Dirac semimetal with linear dispersion along all three momentum directions and can be viewed as a three-dimensional analogue of graphene. By breaking of either time-reversal symmetry or spatial inversion symmetry, the Dirac semimetal is believed to transform into a Weyl semimetal with an exotic chiral anomaly effect, however the experimental evidence of the chiral anomaly is still missing in Cd3As2. Here we show a large negative magnetoresistance with magnitude of -63% at 60 K and -11% at 300 K in individual Cd3As2 nanowires. The negative magnetoresistance can be modulated by gate voltage and temperature through tuning the density of chiral states at the Fermi level and the inter-valley scatterings between Weyl nodes. The results give evidence of the chiral anomaly effect and are valuable for understanding the Weyl fermions in Dirac semimetals.

Dirac and Weyl Semimetal in XYBi (X = Ba, Eu; Y = Cu, Ag and Au)

Weyl and Dirac semimetals recently stimulate intense research activities due to their novel properties. Combining first-principles calculations and effective model analysis, we predict that nonmagnetic compounds BaYBi (Y = Au, Ag and Cu) are Dirac semimetals. As for the magnetic compound EuYBi, although the time reversal symmetry is broken, their long-range magnetic ordering cannot split the Dirac point into pairs of Weyl points. However, we propose that partially substitute Eu ions by Ba ions will realize the Weyl semimetal.

Evidence for the chiral anomaly in the Dirac semimetal Na₃Bi

In a Dirac semimetal, each Dirac node is resolved into two Weyl nodes with opposite "handedness" or chirality. The two chiral populations do not mix. However, in parallel electric and magnetic fields ( E: || B: ), charge is predicted to flow between the Weyl nodes, leading to negative magnetoresistance. This "axial" current is the chiral (Adler-Bell-Jackiw) anomaly investigated in quantum field theory. We report the observation of a large, negative longitudinal magnetoresistance in the Dirac semimetal Na3Bi. The negative magnetoresistance is acutely sensitive to deviations of the direction of B: from E: and is incompatible with conventional transport. By rotating E: (as well as B: ), we show that it is consistent with the prediction of the chiral anomaly.

Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σ_αβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.

Magnetotransport of single crystalline NbAs

We report transport measurement in zero and applied magnetic field on a single crystal of NbAs. Transverse and longitudinal magnetoresistance in the plane of this tetragonal structure does not saturate up to 9 T. In the transverse configuration (H ∥ c, I ⊥ c) it is 230,000% at 2 K. The Hall coefficient changes sign from hole-like at room temperature to electron-like below ∼150 K. The electron carrier density and mobility calculated at 2 K based on a single band approximation are 1.8 × 10(19) cm(-3) and 3.5 × 10(5) cm(2) Vs(-1), respectively. These values are similar to reported values for TaAs and NbP, and further emphasize that this class of noncentrosymmetric, transition-metal monopnictides is a promising family to explore the properties of Weyl semimetals and the consequences of their novel electronic structure.

Topology and interactions in a frustrated slab: tuning from Weyl semimetals to C>1 fractional Chern insulators

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates.

Quantum transport of disordered Weyl semimetals at the nodal point

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.