Large Magnetoresistance in Topological Insulator Candidate TaSe3

Large unsaturated magnetoresistance (XMR) with magnitude 1000% is observed in topological insulator candidate TaSe3 from our high field (up to 38 T) measurements. Two oscillation modes are detected associated with the bulk pockets from our Shubnikov-de Hass (SdH) measurements, consistent with our first-principles calculations. However, our SdH measurements fails to determine the existence of topological surface states in TaSe3, calling for more powerful means to detect on this compound. Moreover, our two-band model analysis exhibits that an imperfect density ratio nh/ne is around 0.9 accounts for XMR at T below 20 K. At T above 20 K, a sudden change of density of carriers suggests a reconstruction of the Fermi surface. Thus, TaSe3 may provide an opportunity to allow us to observe XMR in a topological insulator and to exploit the potential interplay between the XMR and topological surface states for the first time.

Nevertheless, XMR has yet been found in any topological insulators, such as Bi 2 Se 3 family [25], PbSn 1-x Se x [26], BiTeI [27][28][29]. It is not hard to understand because the bulk states remains insulating at the Fermi surface for a typical topological insulator [30]. Even in an n-doped or p-doped case, the lack of XMR could be interpreted as a result of the absence of the coexistence of both hole and electron types of carriers.
Interestingly, a kind of material named TaSe 3 with bulk semimetallic states was recently predicted to be a strong topological insulator candidate [31]. It is a quasi-one-dimensional trichalcogenide with space group P2 1 /m (No. 11) and the crystal structure are shown in Fig. 1(a). In previous works, single crystal TaSe 3 yields a residual resistance ratio (RRR) around 20 [32] and TaSe 3 nanowires claims a low resistivity and high breakdown current density [33][34][35]. In addition, TaSe 3 mesowires possibly host a charge density wave (CDW) at 65 K [36]. Thus, TaSe 3 may provide an opportunity to allow us to observe XMR in a topological insulator and exploit the potential interplay between the XMR and topological surface states for the first time.
Here, we systematically investigate the electronic structure of TaSe 3 and its corresponding transport behavior in this material by combining the first-principles calculations and low-temperature and high-field transport measurements. Unsaturated XMR with magnitude ∼10 3 % is observed from our high field (up to 38 T) measurements. Besides, two oscillation modes are detected associated with the bulk pockets from our SdH measurements, consistent with our first-principles calculations, indicating a topologically trivial electronic structure in bulk. Moreover, our two-band model analysis exhibits that an imperfect density ratio / ≈ 0.9 accounts for XMR when T< 20 K. When temperature increasing to 20 K, a sudden change of density of carriers suggests a reconstruction of the Fermi surface. However, our SdH measurements fail to determine the existence of topological surface states in TaSe 3 compound, calling for more powerful means to detect on this TaSe 3 compound in the future.

A. First-principles calculations
The first-principles calculations were performed using the Vienna ab-initio simulation package (VASP) [37,38]and the generalized gradient approximation with the Perdew-Burke-Ernzerhof (PBE) [39,40] type exchange correlation potential adopted the energy cutoff fixed to 500 eV. The lattice constant a = 9.829 Å, b = 3.495 Å, c = 10.402 Å, α = γ = 90 • , β = 106.26 • , and the ionic positions were relaxed until the energy tolerance was less than 10 -6 eV. In order to obtain the accurate band gap, we adopted a modified Becke-Johnson (mBJ) exchange potential [41] at the meta-GGA level. The k-point sampling grid of the Brillouin zone in the self-consistent process was a Γ-centered Monkhorst-Pack k-point mesh of 6 × 15 × 5, and a total energy tolerance 10 -7 eV was adopted for self-consistent convergence. In order to compute the surface density of states, the tight-binding model of Ta−d and Se−p orbitals was constructed by the maximally localized Wannier functions (MLWF) [42,43] and the surface density of states was obtained by the Wannier Tools package [44] based on the iterative Green's function method [45,46].
We performed the first-principles calculations in order to obtain the basic understandings of the topological nature of electronic structure as well as the Fermi pockets of TaSe 3 . Fig. 1(b) displays the calculated band structure without spin-orbit coupling (SOC), noticing that a band crossing can be identified as marked by the dashed rectangle. The crossing points are gapped when inducing SOC as displayed in direction are presented in the right panel of Fig. 1(d).

B. Crystal growth and characterizations
To experimentally investigate the transport properties of this topological insulator candidate TaSe 3 , single crystals were synthesized via chemical vapor transport (CVT) method. Ta, Se powders were mixed in a ratio of 1:3 and a proper excess of Se was used as transport agent. The mixture was vacuum sealed in a quartz tube, and then heated up to high temperature with a gradient from 1000 °C to 600 °C in a two-zone furnace and kept for one week. Then the furnace was naturally cooled down and the ribbon-like crystals were obtained with typical dimensions of 5 mm × 0.1 mm × 0.05 mm, where the longest dimension corresponds to crystallographic b axis (along the Ta-Ta chains).
The chemical components of the obtained TaSe 3 crystals were identified by the energy dispersive spectrum (EDS), as shown in Fig. 2 Fig. 2(b), which is consistent with the previous study [34,36,48]. Transport measurement was also carried out in our TaSe  Property Measurement System (Quantum Design) with lowest temperature of 2 K and largest magnetic field of 9 T. We measured the temperature dependence of resistance of TaSe 3 samples, as displayed in Fig. 2(c). The resistance dramatically decreases when cooling down, displaying a metallic behavior with residual resistivity ratio (RRR) (300 K)/ (2 K) = 23, which is similar to the literature [32].

C. Quantum oscillations
We then carried out the magneto-transport measurement of our samples under high magnetic field up to 38 T. Fig. 3 Fig. 3(b). One can clearly finds out that the oscillations follow a period proportional to 1/B, confirming that this is the SdH oscillations caused by the formation of Landau-levels under a high magnetic field.
By fast Fourier transformation (FFT) based on the oscillation components displayed in Fig. 3(b), two major peaks with frequency of = 99 T and = 173 T, which correspond to two oscillation modes, are uncovered, as shown in Fig. 3(c). Thus, there are at least two carrier pockets near the Fermi surfaces contributing to the SdH oscillations in TaSe 3 , consistent with the prior theoretical [31] and experimental [49] reports that both oscillation modes are associated with the bulk pockets near the Fermi surface. In general, the SdH oscillations can be well described by the Lifshitz-Kosevich (LK) formula [50], The thermal damping factor is = The effective mass * can be extracted by fitting the temperature dependence of the corresponding oscillation amplitude to , as shown in Fig. 3(d), having * = 0.63 and * = 0.75 . Since there are two oscillation modes in this material, the other related parameters, such as Dingle temperatures, quantum mobilities, etc., need to be extracted by the multiband LK formula [51,52], as depicted in Fig. 3(f). The parameters extracted from the multiband LK fit at 0.36 K, together with the ones obtained from the analysis of SdH oscillations discussed above, are put in Table I.
Specifically, to verify the Berry phase of each oscillation mode, we separate the components from and modes by FFT filter, and then plot the corresponding Landau fan diagram of each mode respectively in Fig. 3(e). Then we obtain the intercepts at n axis of -0.03 and -0.02, respectively, which are both near to zero, indicating the zero Berry phases. These results are the same as the ones got from LK fitting process as seen in Table I

D. Hall measurements
Despite the failure to detect the topological surface states in TaSe 3 from SdH quantum oscillations measurements directly, the fascinating non-saturated XMR behavior is observed in this topological insulator candidate, motivating us to exploit the exotic physics of magnetoresistance in this system. As a result, we performed the detailed Hall measurements on this compound under a relatively low field up to 9 T. Thus, the Hall response was then further analyzed by the isotropic two-band model, which was usually used to identify the transport contributions from hole-like and electron-like carriers [11,53,54]. The conductivity tensor in this model, is given in a complex representation [3]:  Fig. 4(e), stays approximately 0.9 when temperature less than 20 K. As the temperature increases above 20 K, the ratio gradually drops and reaches about 0.65 at 60 K. The imperfect but balanced enough ratio of carriers could cause considerable compensation between electrons and holes, which may account for the non-saturated XMR at low temperature in TaSe 3 . In previous theoretical calculations, the ratio of two types of carriers / ≈ 0.9 can result in a XMR reaching the magnitude of 10 4 % before saturation [2], thus it is understandable to attribute the non-saturated MR behavior to the compensation of two types of carriers.
The difference of the magnitude between our data and the theoretical estimation is probably due to the low mobility of carriers [18,55]. In addition, a sudden decrease of densities of both types of carriers as the temperature increases to 30 K appears, suggesting a reconstruction of the Fermi surface, which may be associated with the possible structural phase transition, such as the potential CDW transition reported recently [36].

III. CONCLUSIONS AND PERSPECTIVE
In summary, we carried out systematic investigation on the electronic structure and the corresponding transport behavior for TaSe