We measure the electrical resistivity ρ of type-II Weyl semimetal WTe2 using high-quality single crystals for the current I along the a and b crystallographic directions in rotating magnetic fields in the plane perpendicular to the current direction. In zero field, ρ exhibits huge anisotropy and the ratio ρb/ρa develops with decreasing temperature approaching ∼30 at T = 0. A low-T power-law behavior of ρ∝Tn with n = 2.7-2.9 may reflect the characteristic carrier scattering mechanism, probably associated with the strongly T-dependent mobilities, which lead to the sign change in the Hall resistivity. In the Kohler plot, the magnitude of the transverse magnetoresistance (MR) differs by more than two orders of magnitude depending on the I- and B-directions. It also shows clear deviation of MR from the B2 dependence for all the configurations. No singular directions (magic angles) appear in the rotating B measurements.
The quantum topological materials, including graphene, Dirac and Weyl semimetals, have attracted considerable attention in recent years because they exhibit novel physical properties.1–4 In this progress, compensated semimetal Tungsten ditelluride (WTe2) has been reported for huge magnetoresistance (MR) and high carrier mobility.5 Theoretically, WTe2 has been predicted as a type-II Weyl semimetal.6 This conjecture has later been confirmed by the observation of the Fermi arcs in ARPES studies.7–10 Interesting features of the electronic state of WTe2 have been reported by the measurements of the pressure effect on MR,11–14 the Fermi surface topology (using quantum oscillations of resistivity, Seebeck and Nernst coefficients),12 the pressure-induced superconductivity and structural instability,15,16 and Raman scatterings.17
In this study, to investigate the anisotropy of the electronic state of Weyl semimetal WTe2, we have measured the electrical resistivity of high-quality single crystals for different current directions in applied magnetic fields, which are rotated in the plane perpendicular to the current direction.
Single crystals of WTe2 were obtained by Te-flux growth technique. Tungsten powder (99.99%) were mixed with excessive amount of Tellurium (99.999%) and placed in an alumina container, then sealed in an evacuated quartz tube. The mixing and grinding was executed in high-purity argon filled glove box. The sealed quartz ampoule with mixture compound was heated in a furnace up to 1050 oC with a rate of 100 oC/h, followed by keeping the temperature at 1050 oC for 10 h. After cooling down to 750 oC at a rate of 1 oC/h, it was inverted and quickly spun into a centrifuge to remove the excess Te flux. Powder X-ray diffraction measurement was performed using a Rigaku Smart lab. For measurements with the current flow for I//a and I//b, two samples were cut out next to each other from a piece of a single crystal. The size (length×width×thickness) is 2.85×0.458 ×0.052 mm3 for I//a and 0.829×0.458×0.052 mm3 for I//b. The distance between the voltage contacts is 1.652 and 0.351 mm for I//a and I//b, respectively. Gold wires were soldered with spot welding to minimize contact resistivity. The electrical resistivity was measured by the four-probe technique using a Quantum Design Physical Properties Measurement System (PPMS-9T).
RESULTS AND DISCUSSION
The room-temperature powder XRD pattern of some pieces of WTe2 single crystals is shown in Fig. 1. The Rietveld refinement confirms that WTe2 crystallizes in the orthorhombic noncentrosymmetric structure (see the inset of Fig. 1) with the space group Pmn21 (#31). The refined lattice parameters are a = 3.458 Å, b = 6.529 Å and c = 14.038 Å, which match well with the earlier report.15 The grown single crystals have a plate-like shape with a typical size of ∼4×0.5×0.2 mm3 as shown in the inset of Fig. 1.
Figure 2(a) shows the temperature dependence of the resistivity ρa for I//a and ρb for I//b in a logarithmic scale. Both of ρa and ρb decrease continuously with decreasing temperature. The ρa-vs-T data shows a huge residual resistance ratio RRR=ρ(300 K)/ρ(T→0)=1330, which is in the highest class in the literature.5,11–14,18 The temperature dependences of the normalized resistivity ρ(T)/ρ(300 K) and the ratio ρb/ρa are shown in Figs. 2(b) and (c). The ratio ρb/ρa is about 8 at room temperature and increases with decreasing temperature approaching ∼30 at T = 0.
The resistivity in the low temperature range below 20 K can be fitted well with the expression ρ(T)=ρ00 + ATn, where ρ00 ≡ ρ(T=0) in zero field, with n = 2.7 and 2.9 for ρa, and ρb, respectively. These values of n, which are clearly different from n = 2 (5) expected theoretically for electron scattering by electrons (phonons),19 may suggest that interband s−d electron phonon scattering, rather than the intraband s−s electron phonon scattering, is dominant at low temperatures.20 Note that similar values of n have been reported for unconventional semimetals LaBi (n = 2.99), ZrSiS (n = 3), and LaSb (n = 4).21–23
Recently, we have found that the Hall resistivity ρxy shows a sign change at 3 K (ρxy>0 below 3 K and ρxy<0 above 3 K) in low fields.24 Using the simple two-carrier model, we have demonstrated that the T- and B-dependent ρxy data indicate that electron and hole mobilities show anomalously strong T dependence below 10 K.24 Furthermore, we have found that significant deviation from Kohler’s rule appears below 10 K,25 indicating wave-vector k dependent anisotropic carrier scattering, which develops with increasing temperature. We expect that these transport anomalies may be associated with the present finding of the anomalous power-law exponent n = 2.7 and 2.9 in ρ∝Tn.
The field dependence of transverse magnetoresistance MR ≡ Δρ/ρ0 ≡ (ρ(T,B) – ρ0)/ρ0, where ρ0= ρ(T, B=0), measured at 2 K is shown in Fig. 3(a) for the current I//a in applied fields B//c and B//b and in Fig. 3(b) for I//b in B//c and B//a. Shubnikov-de Haas (SdH) quantum oscillations appear in high field region. The data do not exhibit any saturation tendency for all the configurations. In 9 T, MR for I//a and B//c reaches 1.5×104, indicating roughly that ωcτ reaches of the order of 104, where ωc and τ represents the cyclotron frequency and the relaxation time of carriers, respectively. In comparison with the earlier reports,5,11–14,18 such high value of MR reflects the high quality of our single crystal. The data demonstrate that MR is extremely anisotropic; the MR values at 9 T are summarized in Table I.
|.||I//a .||I//b .|
|MR (B//a) at 9T||—||400|
|MR (B//b) at 9T||836||—|
|MR (B//c) at 9T||15000||4000|
|.||I//a .||I//b .|
|MR (B//a) at 9T||—||400|
|MR (B//b) at 9T||836||—|
|MR (B//c) at 9T||15000||4000|
In the measured field range, overall behavior of MR seems to show ∼B2 dependence, which is expected for a metal with the carrier compensation, i.e., the electron and hole carrier densities are equal (ne = nh).26 Detailed analysis of the MR behaviors can be made using a so-called Kohler plot, Δρ/ρ0 vs B/ρ0, which is shown in Fig. 3(c). The data show a slight deviation from the B2 dependence. Figure 3(d) shows a Δρ/ρ0/(B/ρ0)2=Δρ×ρ0/B2 vs B plot. If Δρ/ρ0∝B2, this quantity becomes a B independent constant. The value of Δρ×ρ0/B2 gradually decreases with increasing field, clearly demonstrating significant deviation from the B2 dependence.
Such deviation from the B2 dependence can be caused by (1) slight carrier uncompensation, i.e., ne ≠ nh, and (2) inter-Fermi-pocket scattering as discussed for Cd metal.27 In the former case, however, in a simple two carrier model,26 a deviation from the B2 dependence is expected to be enhanced nonlinearly with increasing field, which is different from our observation, i.e., Δρ×ρ0/B2 decreases gradually. In the latter case, quantitative analysis is not easy. The reason for the deviation from the B2 dependence remains unsolved and needs to be studied further.
We have measured MR at 2 K rotating magnetic field direction with B = 5 T in the plane perpendicular to the current direction (transverse configuration). The results are shown in Figs 4(a–d). For both I//a and I//b, the angle dependence of MR shows a twofold symmetry and it can be nicely reproduced by a simple cosine curve expressed by , where C0 and C2 are fitting parameters, as drawn by the thin black curves. These data suggest the absence of “magic angles”, at which MR shows singular cusps or dips associated with some topological character of the Fermi surface as observed in low-dimensional organic metals.28 This is in line with the band structure calculation,12 which indicate that there exist four small Fermi pockets (two electron and two hole pockets) along the Γ-X direction in the reciprocal space.
We have measured the electrical resistivity ρ of type-II Weyl semimetal WTe2 using high-quality single crystals with RRR=1330 for the current I along the a and b crystallographic directions in rotating magnetic fields in the plane perpendicular to the current direction. In zero field, ρ exhibits huge anisotropy and the ratio ρb/ρa develops with decreasing temperature approaching ∼30 at T = 0. A low-T power-law behavior of ρ∝Tn with n = 2.7-2.9 may reflect the characteristic carrier scattering mechanism in WTe2, which is probably associated with the strongly T-dependent mobilities leading to the sign change in the Hall resistivity and the deviation from the Kohler’s rule. In the Kohler plot, the magnitude of the transverse magnetoresistance differs by more than two orders of magnitude depending on the I- and B-directions. The magnetoresistance data also show clear deviation from the B2 dependence for all the configurations. No singular directions (magic angles) appear in the rotating B measurements.
We gratefully appreciate Prof. Hideyuki Sato for fruitful discussions. We thank our colleague Akira Yamada for his assistance in the measurements. This work was financially supported by JSPS KAKENHI Grant Numbers JP15H03693, JP15H05884, JP16F16028 and JP16K05454.