Introduction

Magneto-transport continues to be an exciting topic in condensed matter physics. Some famous examples include discovering and understanding giant/collosal magnetoresistance1,2,3, integer and fractional quantum Hall effects4,5, Shubnikov-de Haas oscillations6, and weak localization7. In metals with weakly- or non-interacting electrons, the resistance typically increases upon the application of a magnetic field due to the bending of electron trajectories8. Negative magnetoresistance (MR) is only observed in certain circumstances. To exploit these phenomena in applications it is essential to understand the scattering mechanisms involved. Low-carrier-density systems offer an interesting platform to explore the fundamental physics of scattering processes. A recent example is SrTiO3–δ whose T 2-power law in resistivity, characteristic of a Landau Fermi liquid, cannot originate from simple electron-electron scattering, as often has been assumed9. Semimetals can be considered as failed semiconductors with a negative indirect band gap. Consequently, these compensated systems, with approximately equal numbers of electrons and holes, have low effective masses due to the low band filling, which leads to rich magnetotransport phenomena including extremely large positive magnetoresistance (XMR) and ultrahigh mobilities exceeding those found in giant/collosal magnetoresistance systems1,2,3. In addition, notions of topology have extended to semimetals as well. Accidental band crossings protected by symmetry allow electronic structures that are described by a massless Dirac equation. If either time reversal or inversion symmetry is broken, the four-fold (including spin) degenerate Dirac point splits into two Weyl points with opposite chirality. Typical examples are Cd3As210 and Na3Bi11 for Dirac semimetals, and TmPn (Tm = Ta, Nb; Pn = As, P) for Weyl semimetals12. As a result of their exotic electronic structure, such semimetals host Fermi-arc surface states, XMR, Shubnikov-de Haas (SdH) oscillations, non-trivial Berry phases, and other related phenomena13,14,15,16,17,18,19,20. Importantly, Dirac/Weyl semimetals are expected to have negative magnetoresistance when current is parallel to a magnetic field due to the Adler-Bell-Jackiw (ABJ) chiral anomaly mechanism21,22,23,24. The ABJ anomaly is a consequence of the chemical potential changing at each of the Weyl nodes, giving rise to an additional conduction channel, and has been taken as a smoking gun for the existence of a Dirac and/or Weyl semimetal.

If no accidental band crossings occur, can one still consider a semimetal as topologically non-trivial? The answer is yes. Similar to the classification for band insulators, topological indices (v0; v1v2v3) (strong and weak) are still appropriate for a regular semimetal due to the presence of a continuous energy gap between electron-like and hole-like bands. The surface states associated with weak (strong) topological indices are expected to be sensitive (immune) to disorder. Herein, we investigate a novel non-magnetic semimetal TaAs2 that is homologous to the OsGe2-type crystalline structure25 respecting inversion symmetry (Fig. 1a). Magnetotransport measurements manifest a nearly compensated semimetal with low carrier density (~1019 cm−3), high mobility (~103 cm2/Vs) and unsaturated XMR (~4,000,000% at 65 T and 0.5 K). Further, angular dependent longitudinal magnetoresistance (LMR) measurements show pronounced negative MR (~−98%), which suggests involvement of a ABJ chiral anomaly. Our first-principles calculations based on Density Functional Theory (DFT) confirm the semimetallicity of TaAs2 but finds no evidence for a Dirac-like band-crossing. Instead, by computing the indices, (0;111), TaAs2 is found to be a “weak” topological material in all three reciprocal lattice directions but not a “strong” topological material. Consequently, TaAs2 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 TaAs2 also illustrates that the scattering mechanisms in (topological) semimetals are still not sufficiently understood.

Figure 1: Crystalline structure of TaAs2 and sample characterization.
figure 1

(a) Crystalline structure of TaAs2. (b) A side view of TaAs2 along (010)-axis. (c), A photograph of TaAs2 single crystal on millimeter-grid paper. (d), A representative EDS spectrum of TaAs2. The inset shows the SEM image of the same sample.

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Results

Figure 1a shows the crystalline structure of TaAs2. 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 TaAs2 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.

Table 1 Crystalline lattice parameters of TaAs2.
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In the absence of magnetic field, TaAs2 shows a metallic Fermi-liquid-like ρxx(T) profile, with a large residual resistivity ratio RRR ≡ ρxx(300 K)/ρxx(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, ρxx(T) turns up and exhibits insulating-like behavior before it levels off at low temperature. Similar behavior is observed in other semimetallic materials26,27,28. 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 Cd3As229 and the Weyl semimetals TmPn15,16,18,19, 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 WTe228, a candidate type-II Weyl semimetal30.

Figure 2: Transport properties of TaAs2.
figure 2

(a) Temperature dependencies of at selected magnetic fields. The inset shows RRR and Fermi liquid behavior at B = 0. (b) Unsaturated MR up to 65 T at 0.5 K. The inset demonstrates quadratic-like MR(B). (c,d) field dependent MR at various temperatures. The inset to c shows MR vs. B2 at 0.3 K. (e,f) Field dependent at various temperatures. The inset to (e) displays a two-band fit of at 0.3 K. The inset to f displays the Hall coefficient RH as a function of T.

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In Fig. 2e,f, we present Hall effect data. For all temperatures measured, the field-dependent Hall resistivity is strongly non-linear and changes from positive at low field to negative at high field. The non-linearity of is reflected further by the divergence between the Hall coefficients RH(0) and RH(9 T) as shown in the inset to Fig. 2f. Here, RH(9 T) is defined by at B = 9 T, and RH(0) is the initial slope of near B = 0. All these features are characteristic signatures of multi-band effects. Indeed, can be well fit to a two-band model,

where n and μ are respectively carrier density and mobility, and the subscript e (or h) denotes electron (or hole). A representative fit to at T = 0.3 K is shown in the inset to Fig. 2e, and from this fit we obtain ne = 1.4(2) × 1019 cm−3, nh = 1.0(1) × 1019 cm−3, μe = 1.9(2) × 103 cm2/Vs, and μh = 2.5(2) × 103 cm2/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 TaAs2 to be a semimetal. Furthermore, the imbalance between ne and nh implies that it is not a perfectly compensated semimetal31.

One important feature of topological Dirac/Weyl semimetals is the so-called ABJ chiral anomaly23,24. 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., σx ∝ B2, observable as a negative LMR20,24. 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 Na3Bi20 and TmPn15,19, the one seen in TaAs2 is bigger in magnitude and survives at much larger ϕ and higher T. For example, Fig. 3c plots 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 systems15,19,20, because increases as B2 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 nt( = ne + nh) = 2.4 × 1019 cm−3, we estimate the average transport mobility  = 1.0 × 107 cm2/Vs. Using the Fermi-surface parameters of the electron-pocket as an example (see SI II), we further calculate the Fermi velocity vF = 7.9 × 105 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 3: Longitudinal magnetoresistance (LMR) of TaAs2.
figure 3

(a) Field-dependent MR of TaAs2 with various angles ϕ at 2 K. The inset shows the configuration of the measurements. (b) MR at different temperatures, measured at ϕ = 0. The inset displays the data at 300 K. (c) The angular dependence of at 2 K and 1 T. (d) A polar plot of MR at 2 K. (e) MR with two different measurement geometries, R32,14 = V14/I32 (red) and R14,32 = V32/I14 (blue). Schematic sketches of the geometry are shown in the insets. (f) Theoretical fits of and . The high-field part of is fit to (blue), and the low-field part is fit to (red). The measurements were done in the contact geometry as shown in the inset to (a).

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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 electron- and hole-bands. Figure 4b shows the Fermi surface (FS) topology calculated with SOC. The FS of TaAs2 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 points30. 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.

Figure 4: DFT calculations of TaAs2 with SOC.
figure 4

(a) Band structure and DOS of TaAs2. (b) FS topology and TRIM points. (c) Parity of the TRIM at the monoclinic Brillouin zone.

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Discussion

Due to the continuous gap in the band structure, the indices can be computed. The presence of inversion symmetry allows us to compute the topological indices (v0; v1v2v3) 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 v0. As can be seen from Fig. 4c, the electronic structure is trivial from this perspective. Nevertheless, all three “weak” topological indices (v1,2,3) 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 TaAs2 is non-magnetic, a magnetic origin can be ruled out. Second, weak localization is also excluded, because 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 PdCoO233 with high FS anisotropy. To test the role of FS anisotropy, we measured the magnetoresistances of R32,14 and R14,32 with the schemes shown in the insets to Fig. 3e. In the measurements of R32,14, the current is parallel to B, and we derived a negative LMR, but the MR of R14,32 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” effect8,34,35,36. 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 Δσxx(B) = σxx(B) − σxx(0) = in the inset to Fig. 3f. The low field part of Δσxx can be well fitted to the form C3B2 (red line), which is consistent with an ABJ chiral conductivity σx. The absence of Dirac or Weyl points in TaAs2, 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 as shown in the main frame of Fig. 3f (red line). At high field, this fitting is gradually violated due to the emergence of a weak parabolic term in , for which we successfully fitted to the formula (blue line). This weak positive MR is probably due to a small angular mismatch that causes a parabolic MR(B) which becomes dominant as field strengthens (See also in SI V).

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 states37, 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 TaAs2, this work calls for future theoretical and experimental work.

In summary, we find that single crystals of TaAs2 grown by vapor transport are semimetals with extremely large, -unsaturating transverse magnetoresistance characteristic of high mobilities. Strikingly, TaAs2 hosts a negative longitudinal magnetoresistance that reaches −98%. TaAs2 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 OsGe2-type TmPn2 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.

Note added: When completing this manuscript, we became aware of several other related works38,39,40,41.

Methods

Sample synthesis and characterization

Millimeter-sized single crystals of TaAs2 were obtained as a by-product of growing TaAs by means of an Iodine-vapor transport technique with 0.05 g/cm3 I2. 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 TaAs2 single crystals with apparent monoclinic shape were picked from the resultant and their monoclinic structure25 and stoichiometry were confirmed by x-ray diffraction (XRD) and energy dispersive x-ray spectroscopy (EDS). No I2 doping was detected, and the stoichiometric ratio is fairly homogenous.

Measurements

Three TaAs2 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 () and Hall resistivity (, 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. () 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 code42 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 TaAs2 was obtained from Rietveld refinement (Table 1).

Additional Information

How to cite this article: Luo, Y. et al. Anomalous electronic structure and magnetoresistance in TaAs2. Sci. Rep. 6, 27294; doi: 10.1038/srep27294 (2016).