Negative magnetoresistance in Weyl semimetals NbAs and NbP： Intrinsic chiral anomaly and extrinsic effects

Chiral anomaly-induced negative magnetoresistance （NMR） has been widely used as critical transport evidence for the existence of Weyl fermions in topological semimetals. In this mini-review, we discuss the general observation of NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can arise from the intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as the superimposition of Hall signals; field-dependent inhomogeneous current flow in the bulk, i.e., current jetting; and weak localization （WL） of coexistent trivial carriers. The WLmcontrolled NMR is heavily dependent on sample quality and is characterized by a pronounced crossover from positive to negative MR growth at elevated temperatures, resulting from the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation between the NMR and the chiral anomaly need to be scrutinized without the support of complimentary techniques. Because of the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, which is a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping with magnetic and non-magnetic impurities is thus more convincing than the NMR method for detecting the existence of Weyl fermions.

Doping-enhanced robustness of anomaly-related magnetoresistance in WTe_(2±α)flakes

We study systematically the negative magnetoresistance(MR)effect in WTe_(2±α)flakes with different thicknesses and doping concentrations.The negative MR is sensitive to the relative orientation between electrical-/magnetic-field and crystallographic orientation of WTe_(2±α).The analysis proves that the negative MR originates from chiral anomaly and is anisotropic.Maximum entropy mobility spectrum is used to analyze the electron and hole concentrations in the flake samples.It is found that the negative MR observed in WTe_(2±α)flakes with low doping concentration is small,and the high doping concentration is large.The doping-induced disorder obviously inhibits the positive MR,so the negative MR can be more easily observed.In a word,we introduce disorder to suppress positive MR by doping,and successfully obtain the negative MR in WTe_(2±α)flakes with different thicknesses and doping concentrations,which indicates that the chiral anomaly effect in WTe_(2)is robust.

Symmetry transformation of nonlinear optical current of tilted Weyl nodes and application to ferromagnetic MnBi_(2)Te_(4)

A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.

Negative magnetoresistance in Dirac semimetal Cd_(3)As_(2)with in-plane magnetic field perpendicular to current

Topological insulators and semimetals have exotic surface and bulk states with massless Dirac or Weyl fermions,demonstrating microscopic transport phenomenon based on relativistic theory.Chiral anomaly induced negative magnetoresistance(negative MR)under parallel magnetic field and current has been used as a probable evidence ofWeyl fermions in recent years.Here we report a novel negative MR result with mutually perpendicular in-plane magnetic field and current in Cd_(3)As_(2)nanowires.The negative MR has a considerable value of-16%around 1.5 K and could persist to room temperature of 300 K with value of-1%.The gate tuning and angle dependence of the negative MR demonstrate the mechanism of the observed negative MR is different from the chiral anomaly.Percolating current paths induced by charge puddles and disorder might be involved to produce such considerable negative MR.Our results indicate the negative MR effect in topological semimetals involves synergistic effects of many mechanisms besides chiral anomaly.

Nonlinear current response and electric quantum oscillations in the Dirac semimetal Cd_(3)As_(2)

Chiral anomaly is a distinct quantum anomaly associated with chiral fermions in Dirac or Weyl semimetals.The use of negative magnetoresistance(negative MR)as a signature for this anomaly remains contentious,as trivial mechanisms such as current jetting and weak localization can also induce negative MR.In this study,we report a novel nonlinear behavior of the chiral anomaly in the longitudinal direction,which we observed by applying parallel current and magnetic field to the Dirac semimetal Cd_(3)A_(s_(2)).This nonlinear characteristic peaks at an intermediate magnetic field of approximately5 T,displaying a resistance-increasing property concomitant with strengthening of the current source.Through angledependence experiments,we were able to rule out trivial factors,such as thermal effects,geometric artifacts,and anisotropy.Furthermore,additional electric quantum oscillations were observed when the direct current(DC)was applied as high as300μA.Such an unusual phenomenon is ascribed to the formation of quantized levels due to Bloch oscillation in the high DC regime,suggesting that an oscillatory density distribution may arise as the electric field increases.The non-Ohmic electric quantum oscillations open a new avenue for exploring chiral anomaly and other nontrivial topological properties,which is also one of the salient features of nonequilibrium steady states in condensed matter physics.

Recent observations of negative longitudinal magnetoresistance in semimetal

The discovery of Dirac semimetal and Weyl semimetal has motivated a growing passion for investigating the unique magneto-transport properties in the topological materials.A Weyl semimetal can host Weyl fermions as its low-energy quasi-particle excitations,and therefore perform exotic features analogous to those in high-energy physics,such as the violation of the chiral charge conservation known as the chiral anomaly.One of the electrical transport signatures of the chiral anomaly is the Adler-Bell-Jackiw（ABJ） anomaly which presents as a negative magnetoresistance when the magnetic field and the current are parallel.Very recently,numerous experiments reported negative longitudinal magnetoresistance（NLMR） in topological materials,but the details of the measurement results are various.Here the materials and the corresponding experiment results are briefly reviewed.Besides the plausible explanation of the ABJ anomaly,some other origins of the NLMR are also discussed.

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topo- logical semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity nmy not be a com- pelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.

Evidence for a Dirac nodal-line semimetal in SrAs_3

Dirac nodal-line semimetals with the linear bands crossing along a line or loop, represent a new topological state of matter. Here, by carrying out magnetotransport measurements and performing first-principle calculations, we demonstrate that such a state has been realized in high-quality single crystals of SrAs_3.We obtain the nontrivial ∏ Berry phase by analysing the Shubnikov-de Haas quantum oscillations. We also observe a robust negative longitudinal magnetoresistance induced by the chiral anomaly.Accompanying first-principles calculations identifies that a single hole pocket enclosing the loop nodes is responsible for these observations.