Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs

Weyl semi-metal is the three dimensional analog of graphene. According to the quantum field theory, the appearance of Weyl points near the Fermi level will cause novel transport phenomena related to chiral anomaly. In the present paper, we report the first experimental evidence for the long-anticipated negative magneto-resistance generated by the chiral anomaly in a newly predicted time-reversal invariant Weyl semi-metal material TaAs. Clear Shubnikov de Haas oscillations (SdH) have been detected starting from very weak magnetic field. Analysis of the SdH peaks gives the Berry phase accumulated along the cyclotron orbits to be {\pi}, indicating the existence of Weyl points.

parallel magnetic and electric fields (12). For any realistic lattice system, the chiral anomaly then manifests itself in the inter-valley pumping of the electrons between Weyl points with opposite chirality. In the non-interacting case, the chiral anomaly can be simply ascribed to the zeroth Landau levels, which are chiral and have opposite sign of the velocity for states around Weyl points with opposite chirality, as shown in Fig. 1D (12). The additional electric field parallel to the magnetic field will then generate imbalance between two chiral modes leading to electric current which can only be balanced by inter-valley scattering. Considering the facts that for clean samples the inter-valley scattering time is extremely long and the degeneracy of the Landau level is proportional to the magnetic field strength, the chiral anomaly in WSM will in general lead to negative magneto-resistance ( = ( ( ) − (0)) (0) ⁄ ) when the magnetic field is parallel to the current. On the other hand, for ordinary metal or semiconductors the MR is weak, positive and usually not very sensitive to the magnetic field direction. Therefore, the negative and highly anisotropic MR has been regarded as the most prominent signatures in transport for the chiral anomaly and indicates the existence of 3D Weyl points.
Besides, chiral anomaly can also generate other fascinating phenomena, i.e. the anomalous Hall effect and nonlocal transport properties (6,13).
Using first principle calculations, Weng et al. (24) predicted that a family of binary compounds represented by TaAs are time-reversal invariant 3D WSMs with a dozen pairs of Weyl nodes which are generated by the absence of inversion center. Materials in TaAs family are completely stoichiometric and nonmagnetic, providing an almost ideal platform for the study of chiral anomaly in WSM. In this work, we perform transport studies of the TaAs single crystal down to 1.8 K with magnetic field up to 9 T. Ultrahigh mobility (µ e ≈1.8×10 5 cm 2 V -1 s -1 at 10 K) has been found with multiband character. Extremely large positive MR (≈ 80000％ at 1.8 K in a field of 9 T) has been discovered for magnetic field perpendicular to the current (or the external electric field). When the magnetic field is rotated to be parallel to the current, notable negative MR has been observed, demonstrating the chiral anomaly effects in this particular material. Strong SdH oscillations have also been found from very low magnetic field, from which two sets of oscillation frequencies can be extracted indicating two types of carriers, in good consistence with first-principles calculations.
TaAs crystallizes in a body-centered-tetragonal NbAs type structure with nonsymmorphic space group of I4 1 md, in which c-axis is perpendicular to the abplane (See Fig.1A). The lattice parameters are a=b=3.4348 Å and c=11.641 Å (28).
Due to the lack of inversion symmetry, first principle calculations predict a dozen pairs of Wely points in the Brillouin zone (BZ) (24). A schematic diagram of theoretical predicted Weyl nodes projected on the (001) facet can be seen in Fig. 1B.
Single crystals of TaAs studied in this work are synthesized via chemical vapor transport method (See Method). Figure 1C shows the X-ray diffraction from a TaAs  where τ is the inter valley scattering time, v f is the Fermi velocity near the Weyl points and µ denotes the chemical potential measured from the energy of the Weyl points.
The above chiral part of the conductivity increasing quadraticly with magnetic field B leads to negative MR, which has the maximum effect with E parallel to B. Of course the total conductivity of the system will also include other contributions from the nonchiral states as well, which may weaken the negative MR effect or even overwhelm it if the non-chiral part dominates the DC transport. Therefore in order to see the chiral negative MR, the high quality sample with chemical potential close enough to the Weyl point is crucial. In this work, this can be roughly recognized by the coexistence of SdH oscillations and giant transverse MR (See Fig. 2A), which usually implied small Fermi surfaces around Fermi level (30). Further discussions in the following will give quantitative analyses. Measurements are also implemented by tilting the magnetic field with respect to the (001) facet but keeping ⊥ (See Fig. S1b). As expected, no evidence of negative MR phenomenon has been detected and adds to growing evidence that the negative MR origins from the chiral term • .
Near zero field, all the data in Fig. 2B show sharp dips, which may be attributed to the WAL effect stemming from the strong spin-orbit interactions (27), which dominates the transport behavior of the non-chiral states. For magnetic field higher than 9 T, the MR will change sign to be positive again. This behavior is very similar to the situation in Bi x Sb (1-x) (27). Since the separation between the Weyl points in k-space is about 3-8% of the zone boundary (24), which is quite big comparing with the energy scale of the Zeeman coupling, it is very unlikely that the Weyl points will annihilate in pairs in high magnetic field. One possible explanation is due to the Coulomb interaction among the electrons occupying the chiral states. Since the degeneracy of the chiral states as well as the density of states at the Fermi level goes linearly with the magnetic field, eventually the system will approach a spin-density-wave (SDW) like instability under Coulomb interaction (31). Then at finite temperature, the strong SDW fluctuation provides another scattering channel which can be greatly enhanced in high field and may give the positive MR in the high field region.  Fig. 2A). Figure 3A shows the magnetic field dependence of Hall resistivity  xy (B z ) measured at various temperatures. At low temperature, the negative slope in high magnetic fields indicates that the electrons dominate the main transport processes. However, in low fields the curve tends to be flat. Remarkably, we note that, the negative slope of Hall resistivity changes to positive at higher temperature, implying the carriers dominating the conduction mechanism transformed to hole-type. The transition temperature as shown in Fig. 3B is about 100 K. At this temperature, not only the slope, but also the values of Hall resistivity change signs. This signified the possibility of the coexistence of high-mobility electrons with low-mobility holes (30,32,33). Using two-carrier model (32,33), both longitudinal conductivity and Hall conductivity are fitted to estimate the mobility and the concentration of electrons (µ e , n e ) and holes (µ h , n h ) at various temperatures. The results of the temperature dependent fitting parameters are summarized in Fig. 3C and Table S1 oscillations associated with 6 T are too weak in amplitude to be labeled. We note also that  xx (B) has transition from quadratic field dependence at low fields to linear dependence at higher fields. The crossover field strength increases monotonically with the temperature as introduced in more detail in the supplementary (See Fig. S4).
In Fig. 3F the temperature dependence of resistivity  xx at θ=0° is plotted. In zero magnetic field, TaAs exhibits a metallic behavior down to 1.8 K (See the inset of Fig.   3F). The applied magnetic field not only significantly increases the resistivity, but also stimulates a crossover from metallic to insulator like behavior, which may be related to the formation of the Landau levels under magnetic field.
The Combining the information obtained from both quantum oscillation experiments and first principle calculations, we can conclude that it is likely the FS associated with 16 T oscillating frequency encloses the Weyl points W1 and dominate the DC transport in TaAs, which on the other hand strengthens our conclusion that the negative MR observed in this material is truly due to chiral anomaly.
In summary, the transport properties of proposed WSM TaAs have been studied in detail. Our results suggest that there are both n and p types of carrier in TaAs, which nearly compensate to each other. Further analyses of the Hall effect data through twocarrier fittings obtained the electronic motilities at different temperatures and gives out an unexpected high value of µ e ≈1.8×10 5 cm 2 V -1 s -1 for the electrons at 10 K. Giant linear MR as high as 80000% at 9T has been found with magnetic field perpendicular to the current, which is quite similar with the behavior in Dirac semi-metal Cd 3 As 2 .
When the external magnetic field is rotated to be parallel with the current, the MR becomes negative between 1-9 T, with the most negative value to be -30%. This unusual negative MR is the first evidence for the chiral anomaly associated with the Weyl points in TaAs. The π Berry phase acquired by electrons in cyclotron orbits is another strong evidence of Weyl points. Thus, TaAs is the first nonmagnetic compound confirmed by the experiments to host WSM state, which has paved the way for more experimental studies in this completely new research territory.
During preparation of this manuscript the authors became aware of a related work by Zhang et al. posted on arXiv (arXiv:1502.00251 (2015)).

Method
Single crystals of TaAs were grown by chemical vapor transport. A previously reacted polycrystalline TaAs was filled in the quartz ampoule using 2 mg/cm 3