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.

anomaly. Our first-principles calculations based on Density Functional Theory (DFT) confirm the semimetallicity of TaAs 2 but finds no evidence for a Dirac-like band-crossing. Instead, by computing the  2 indices, (0;111), TaAs 2 is found to be a "weak" topological material in all three reciprocal lattice directions but not a "strong" topological material. Consequently, TaAs 2 should host surface states due to its electronic topology. We suggest that the very large negative magnetoresistance is a consequence of this novel topological state. Our observation of negative LMR in TaAs 2 also illustrates that the scattering mechanisms in (topological) semimetals are still not sufficiently understood. Figure 1a shows the crystalline structure of TaAs 2 . It crystallizes in a monoclinic structure with space group C12/m1 (No. 12, symmorphic). There are two chemical sites for As atoms in each unit cell, labeled As1 and As2, respectively. As1 and Ta form Ta-As planes. The interlayer coupling is bridged by As2 atoms, which reside near the central plane along the c-axis (see Fig. 1b). Each Ta atom has eight nearest neighbors: five As1 and three As2. Figure 1c shows a TaAs 2 single crystal with a typical size on millimeter-grid paper. EDS analysis gives the mole ratio Ta:As = 1:1.90 (5), within experimental error consistent with the stoichiometric ratio. By XRD refinement, we deduce the crystalline lattice parameters listed in Table 1. Most importantly, inversion symmetry is respected in this compound.

Results
In the absence of magnetic field, TaAs 2 shows a metallic Fermi-liquid-like ρ xx (T) profile, with a large residual resistivity ratio RRR ≡ ρ xx (300 K)/ρ xx (0.3 K) ≈ 100 (inset to Fig. 2a), manifesting good sample quality. There is no signature of superconductivity above 0.3 K. When a magnetic field is applied, ρ xx (T) turns up and exhibits insulating-like behavior before it levels off at low temperature. Similar behavior is observed in other semimetallic materials [26][27][28] . The insulating-like behavior becomes more and more pronounced as field increases, which leads to an XMR at low temperature. In Fig. 2b, we show MR(B)[≡(R(B) − R(0))/R(0) × 100%] measured at 0.5 K and in fields up to 65 T. The MR reaches ~4,000,000% (~200,000%) at 65 T (9 T), without any signature of saturation. Unlike the linear or sub-linear MR(B) observed in the Dirac semimetal Cd 3 As 2 29 and the Weyl semimetals TmPn 15,16,18,19 , here MR(B) generally obeys a parabolic field dependence (inset to Fig. 2c), although the exponent decreases slightly at very high field (inset to Fig. 2b). Such behavior is reminiscent of WTe 2 28 , a candidate type-II Weyl semimetal 30 .
In Fig. 2e,f, we present Hall effect data. For all temperatures measured, the field-dependent Hall resistivity ρ yx is strongly non-linear and changes from positive at low field to negative at high field. The non-linearity of ρ B ( )  where n and μ are respectively carrier density and mobility, and the subscript e (or h) denotes electron (or hole). A representative fit to ρ B ( ) yx at T = 0.3 K is shown in the inset to Fig. 2e, and from this fit we obtain n e = 1.4(2) × 10 19 cm −3 , n h = 1.0(1) × 10 19 cm −3 , μ e = 1.9(2) × 10 3 cm 2 /Vs, and μ h = 2.5(2) × 10 3 cm 2 /Vs. The carrier densities are close to those estimated from the analysis of SdH oscillations [see Supplementary Information (SI) II]. The low carrier density confirms TaAs 2 to be a semimetal. Furthermore, the imbalance between n e and n h implies that it is not a perfectly compensated semimetal 31 .
One important feature of topological Dirac/Weyl semimetals is the so-called ABJ chiral anomaly 23,24 . The ABJ anomaly is a result of chiral symmetry breaking when B·E is finite. This gives rise to a charge-pumping effect between opposite Weyl nodes. An additional contribution to the total conductivity is generated, i.e., σ x ∝ B 2 , observable as a negative LMR 20,24 . In Fig. 3a, we present the MR(B) at 2 K and various φ (φ is the angle between B and electrical current I). Indeed, we observe a striking negative LMR when φ = 0. The MR reaches −98% before it starts to turn up weakly at high field ( Fig. 3f), which we ascribe to a small angular mismatch (see below). The negative LMR also persists to high temperatures T > 150 K (cf Fig. 3b). Compared with the chiral-anomaly-induced negative LMRs observed in Dirac/Weyl semimetals, such as Na 3 Bi 20 and TmPn 15,19 , the one seen in TaAs 2 is bigger in magnitude and survives at much larger φ and higher T. For example, Fig. 3c plots ρ xx measured at 1 T and 2 K as a function of φ, and the angular dependent MR is sketched in a polar plot in Fig. 3d. Clearly, the negative LMR survives for φ as large as 30°. Note that the cusp near B = 0 is not overcome until φ > 45 (Fig. 3a). In contrast to other systems 15,19,20 increases as B 2 when B⊥I, the slow rate of increase in MR in the vicinity of zero field makes it more robust against angular mismatch. This also allows the negative LMR in the limit of B → 0. Taking only 2% residual resistivity at 3 T and the total carrier density n t ( = n e + n h ) = 2.4 × 10 19 cm −3 , we estimate the average transport mobility µ = 1.0 × 10 7 cm 2 /Vs. Using the Fermi-surface parameters of the electron-pocket as an example (see SI II ), we further calculate the Fermi velocity v F = 7.9 × 10 5 m/s, and transport relaxation time τ = 4.8 × 10 −10 s. This means that the carriers can travel a distance (viz. mean free path) l = 0.4 mm without backward scattering. Such an anisotropic MR and field induced low-scattering state would apparently find applications in electronic/spintronic devices, but the scattering mechanism is an open question. Figure 4a shows the band structure and density of states (DOS) calculated with spin-orbit coupling (SOC). The semimetallic character can be seen by the low DOS at the Fermi level and the presence of small electronand hole-bands. Figure 4b shows the Fermi surface (FS) topology calculated with SOC. The FS of TaAs 2 mainly consists of one hole-and two electron-pockets. The electron-pockets, located off the symmetry plane, are almost elliptical. The hole-pocket encompasses the M point at (1/2, 1/2, 1/2) but is more anisotropic with two extra "legs". The abnormal FS structure of the hole pocket also is reflected in the complicated SdH frequencies discussed in  the SI II. Two additional electron-like pockets with vanishingly small size are observed intersecting the top of the Brillouin zone. Without SOC, accidental band crossings do occur as shown in the SI III , and they can be classified as type-II Dirac points 30 . Upon adding SOC, however, these Dirac points become gapped, and a careful survey over the entire Brillouin zone reveals no accidental band crossings in the vicinity of the Fermi level. The possibility of a Weyl semimetal is in any event excluded due to the preservation of both time reversal and inversion symmetries.

Discussion
Due to the continuous gap in the band structure, the  2 indices can be computed. The presence of inversion symmetry allows us to compute the topological indices (v 0 ; v 1 v 2 v 3 ) based only on the parities of the occupied wave functions at time-reversal-invariant-momenta (TRIM) 32 . The results are shown in Fig. 4c. (Refer to SI IV for more details.) The unoccupied states of the hole band at M do not influence the topological indices because these states have even parity. The product of parities over all the TRIM gives the value of the so-called "strong" topological index v 0 . As can be seen from Fig. 4c, the electronic structure is trivial from this perspective. Nevertheless, all three "weak" topological indices (v 1,2,3 ) are non-trivial. Hence, surface states are mandated by these weak topological indices, although they are believed to be sensitive to disorder. We now return to the issue of the negative LMR. An electric current parallel to a magnetic field is not expected to experience a Lorentz force; however, in reality, negative LMR may exist stemming from a variety of mechanisms. First, because TaAs 2 is non-magnetic, a magnetic origin can be ruled out. Second, weak localization is also excluded, because ρ T ( ) xx conforms to Fermi-liquid behavior at low temperatures, and no −logT or any form of upturn signature can be identified. Third, negative LMR was also observed in materials such as PdCoO 2 33 with high FS anisotropy. To test the role of FS anisotropy, we measured the magnetoresistances of R 32,14 and R 14,32 with the schemes shown in the insets to Fig. 3e. In the measurements of R 32,14 , the current is parallel to B, and we derived a negative LMR, but the MR of R 14,32 is positive. Similar results were reproduced on several other samples with different shapes. Because the direction of current is arbitrary when referenced to the crystalline axes, these measurements imply that the observed negative LMR is locked to the relative angle between E and B, rather than pinned to particular FS axes. Fourth, an improperly made contact geometry may also cause negative LMR especially when the material shows a large transverse MR, known as the "current-jetting" effect 8,34-36 . We have performed a series of careful LMR measurements with different contact geometries, and the results reveal that albeit a current-jetting effect can occur, the large negative LMR, however, is also intrinsic. SI V provides more details.
To study further the features of this negative LMR, we plot Δσ xx (B) = σ xx (B) − σ xx (0) = in the inset to Fig. 3f. The low field part of Δσ xx can be well fitted to the form C 3 B 2 (red line), which is consistent with an ABJ chiral conductivity σ x . The absence of Dirac or Weyl points in TaAs 2 , however, indicates that the negative LMR is not a consequence of the ABJ chiral anomaly as has been posited for other Dirac and Weyl semimetals. The fitting is converted back to ρ B Given the absence of alternative possibilities, an interesting question is whether the presence of topological surface states coexisting with a bulk semimetallic electronic structure could produce the large negative LMR as we observe. We note that conductivity corrections are found when surface states interact with bulk conduction states 37 , although the observed effect here is an increase in the conductivity of a factor of ~50. Having ruled out possible interpretations for the origin of a firmly established large, negative LMR in TaAs 2 , this work calls for future theoretical and experimental work.
In summary, we find that single crystals of TaAs 2 grown by vapor transport are semimetals with extremely large, -unsaturating transverse magnetoresistance characteristic of high mobilities. Strikingly, TaAs 2 hosts a negative longitudinal magnetoresistance that reaches −98%. TaAs 2 is an example of a semimetal whose strong topological index is trivial, yet all three of its weak topological indicies are non-trivial. Similar properties also may exist in other OsGe 2 -type TmPn 2 compounds where Tm = Ta and Nb, and Pn = P, As and Sb. As was the case for giant magnetoresistance, potential applications exist if the scattering mechanisms in these semimetals can be understood and manipulated.

Methods
Sample synthesis and characterization. Millimeter-sized single crystals of TaAs 2 were obtained as a by-product of growing TaAs by means of an Iodine-vapor transport technique with 0.05 g/cm 3 I 2 . First, polycrystalline TaAs was prepared by heating stoichiometric amounts of Ta and As in an evacuated silica ampoule at 973 K for three days. Subsequently, the powder was loaded in a horizontal tube furnace in which the temperature of the hot zone was kept at 1123 K and that of the cold zone was ~1023 K. Several TaAs 2 single crystals with apparent monoclinic shape were picked from the resultant and their monoclinic structure 25 and stoichiometry were confirmed by x-ray diffraction (XRD) and energy dispersive x-ray spectroscopy (EDS). No I 2 doping was detected, and the stoichiometric ratio is fairly homogenous.
Measurements. Three TaAs 2 single crystals (labeled S1, S2 and S3) were polished into a plate with the normal perpendicular to the ab-plane. Ohmic contacts were prepared on the crystal in a Hall-bar geometry, and both in-plane electrical resistivity ( ρ xx) and Hall resistivity ( ρ yx , S1 only) were measured by slowly sweeping a DC magnetic field from −9 T to 9 T at a rate of 0.2 T/min. ρ xx ( ρ yx ) was obtained as the symmetric (antisymmetric) component under magnetic field reversal. An AC-resistance bridge (LR-700) was used to perform these transport measurements in a 3-He refrigerator. Field-rotation measurements were carried out using a commercial rotator on a Physical Property Measurement System (PPMS-9, Quantum Design). Different contact geometries were made on S3 to show a possible current-jetting effect, and the measurements were performed in a 3-axis magnet.
Magnetoresistance also was measured up to 65 T in a pulsed field magnet at the National High Magnetic Field Laboratory (NHMFL, Los Alamos). Several additional samples with different shapes were measured to confirm the reproducibility of negative LMR.
DFT calculations. Density functional theory calculations were performed using the generalized gradient approximation (GGA) as implemented in the WIEN2K code 42 with the exchange correlation potential of Perdew-Burke-Ernzerhof (PBE) 43 . Spin-orbit coupling on all atoms without relativistic local orbitals was included in a second variational scheme. The structure of TaAs 2 was obtained from Rietveld refinement (Table 1).