Superconductivity in Weyl semimetal candidate MoTe2

Transition metal dichalcogenides have attracted research interest over the last few decades due to their interesting structural chemistry, unusual electronic properties, rich intercalation chemistry and wide spectrum of potential applications. Despite the fact that the majority of related research focuses on semiconducting transition-metal dichalcogenides (for example, MoS2), recently discovered unexpected properties of WTe2 are provoking strong interest in semimetallic transition metal dichalcogenides featuring large magnetoresistance, pressure-driven superconductivity and Weyl semimetal states. We investigate the sister compound of WTe2, MoTe2, predicted to be a Weyl semimetal and a quantum spin Hall insulator in bulk and monolayer form, respectively. We find that bulk MoTe2 exhibits superconductivity with a transition temperature of 0.10 K. Application of external pressure dramatically enhances the transition temperature up to maximum value of 8.2 K at 11.7 GPa. The observed dome-shaped superconductivity phase diagram provides insights into the interplay between superconductivity and topological physics.

T ransition metal dichalcogenides (TMDs) have attracted tremendous attention due to their rich physics and promising potential applications [1][2][3][4][5][6][7][8][9][10][11] . TMDs share the same formula, MX 2 , where M is a transition metal (for example, Mo or W) and X is a chalcogenide atom (S, Se and Te). These compounds typically crystallize in many structures, including 2H-, 1T-, 1T 0 -and T d -type lattices. The most common structure is the 2H phase, where M atoms are trigonal-prismatically coordinated by the chalcogenide atoms. These planes then stack on one other with van der Waals gaps inbetween. In contrast, the 1T structure corresponds to octahedral coordination of M. The 1T 0 phase is a monoclinic lattice that can be interpreted as a distortion of the 1T phase by the formation of in-plane M-M bonds, resulting in a pseudohexagonal layer with zigzag metal chains. Finally, the T d phase is very similar to the 1T 0 phase, but the layers stack in a direct fashion, resulting in a higher-symmetry orthorhombic structure. Depending on the synthesis technique, the same composition of MX 2 can crystallize in a variety of structures with very different electronic properties. For example, MoTe 2 exists in 2H, 1T 0 and T d structures [12][13][14] , while WTe 2 has commonly been observed in the T d structure 15 . The 2H and 1T compounds are primarily semiconducting, whereas the 1T 0 and T d compounds are typically semimetallic.
Very recently, semimetallic TMDs have attracted considerable attention because of the discovery of salient quantum phenomena. For instance, T d À WTe 2 has been found to exhibit an extremely large magnetoresistance 16,17 , pressure (P)-driven superconductivity (highest resistive transition temperature T c E7 K at 16.8 GPa) (refs 18,19), and a large and linear Nernst effect 20 . Further, this material has been theorized to constitute the first example of a type-II Weyl semimetal 21 . Moreover, the 1T 0 -MX 2 monolayer has been predicted to be a two-dimensional topological insulator 6 .
The discovery of superconductivity in WTe 2 is apparently contradictory to previous theoretical predictions 22 , which claim that 2H TMDs may become superconducting at high P, but the 1T 0 phases will not. Thus the investigation of other TMDs for the appearance of superconductivity under pressure is of big interest. Molybdenum ditelluride (MoTe 2 ) is unique among the TMDs since it is the only material that can be grown in both 2H and 1T 0 forms, allowing for direct examination of this theory. If superconductivity exists in 1T 0 -MoTe 2 , it may allow the topological edge states to also become superconducting because of the proximity effect in a bulk superconductor. This would open up a new platform for the study of topological superconductivity, which has potential application in quantum computation 23 . Regarding the recently anticipated Weyl semimetal phase in MoTe 2 (ref. 24), discovery of superconductivity may introduce a new pathway for the exploration of topological superconductivity [25][26][27] along with emergent space-time supersymmetry 28 .
Here, we report on the transport properties of the 2H, 1T 0 and T d polytypes of MoTe 2 under various applied P. We find that T d -MoTe 2 exhibits superconductivity with T c ¼ 0.10 K, according to electrical resistivity (r) measurements. Application of relatively low pressures below 1 GPa dramatically enhances the T c , and a dome-shaped T c -P phase diagram is observed with maximum T c ¼ 8.2 K at 11.7 GPa; this is B80 times larger than the ambient pressure value. In contrast, we do not observe any traces of superconductivity in the 2H phase, even when it becomes metallic under P. We assume that the extreme sensitivity of the superconductivity to P is a consequence of the unique electronic structure. Thus, MoTe 2 presents the opportunity to study the interaction of topological physics and superconductivity in a bulk material.

Results
Structure and transport properties at ambient pressure.  (Å 3 ) 1T' [100] samples were structurally characterized ( Fig. 1) using singlecrystal x-ray diffraction (SXRD) and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The atomic arrangement of the 1T 0 structure was determined using high-resolution HAADF-STEM images and diffraction patterns, as shown in Fig. 1a,b and Supplementary  Fig. 1a,b. The crystal structures of 1T 0 and T d -MoTe 2 are sketched in Fig. 1c. At room temperature, the crystals exhibit the expected monoclinic 1T 0 -MoTe 2 structure, while the SXRD measurements at 120 K indicate a transition into the orthorhombic T d structure.
The 1T 0 -MoTe 2 structure crystallizes in the P2 1 /m space group with lattice parameters of a ¼ 6.320 Å, b ¼ 3.469 Å, c ¼ 13.86 Å and b ¼ 93.917°; these results are consistent with the previously reported structure 12 . The Raman spectra at ambient P contain two characteristic peaks ( Supplementary Fig. 1c), which are due to the A g and B g vibrational modes of the 1T 0 -MoTe 2 structure; this is also in agreement with a previous report 29 . A full structural solution was obtained for the orthorhombic T d phase at 120 K, the refined parameters are given in Supplementary  Tables 1 and 2. Temperature dependence of electrical resistivity of MoTe 2 down to a minimum temperature of T min ¼ 0.08 K at ambient pressure is presented in Fig. 2. In contrast to the 2H phase, which displays semiconducting behaviour, 1T 0 -MoTe 2 is semimetallic in nature. At zero field, the room-temperature resistivity is r ¼ 1.0 Â 10 À 5 O m, which decreases to 2.8 Â 10 À 7 O m at 0.25 K, yielding a residual resistance ratio (RRR) E36. At TE250 K an anomaly with thermal hysteresis (Fig. 2a, inset) is observed, which is associated with the first-order structural phase transition from the 1T 0 to the T d polytype 14,30 . A range of magnetotransport properties has been measured at zero pressure on our MoTe 2 crystals (Supplementary Figs 2-4 and Supplementary Note 1). From Hall effect measurements, MoTe 2 shows dominant electron-type transport. Within a single-band model the electron concentration n e is estimated to 5 Â 10 19 cm À 3 at 2 K and 8 Â 10 20 cm À 3 at 300 K ( Supplementary Fig. 2), which is close to reported values 29 . In addition, T d -MoTe 2 gradually becomes superconducting below TB0.3 K (the onset of transition), while zero resistance is observed at T c ¼ 0.10 K (Fig. 2b). Note that, although potential superconductivity atB0.25 K in MoTe 2 has been briefly mentioned in the literature 31 , no related data have been published.
1T 0 -T d structural transition under pressure. It is well known that high pressure can effectively modify lattice structures and the corresponding electronic states in a systematic fashion. Hence, we measured r(T) for the same 1T 0 -MoTe 2 single crystal at various pressure values P (Fig. 3). Figure 3a shows the typical r(T) curves for P up to 34.9 GPa. For increasing P, the metallic characteristic becomes stronger and r decreases over the entire temperature range. At low pressures, resistance curves exhibit an anomaly at a temperature T s , associated with the monoclinic 1T 0 -orthorhombic T d structural phase transition similarly to the ambient pressure data. With pressure increase, the resistivity anomaly becomes less pronounced whereas the temperature of anomaly T s is significantly shifted to lower T and disappears completely above 4 GPa. Thus, the application of P tends to stabilize the monoclinic phase. In addition, the Raman spectra recorded at room temperature under different pressures (Fig. 4a) contain only two characteristic peaks for the 1T 0 -structure A g and B g modes 29 . The frequencies of both vibrational modes increase gradually with no discontinuities as P increases (Fig. 4b) indicating the absence of major structural phase transition in the whole studied pressure range at room temperature. The SXRD data ( Fig. 4c and Supplementary Fig. 5) also indicate that application of pressure stabilizes the monoclinic 1T 0 structure. Increase of P at room temperature results in enhancement of monoclinic distortion (increase of the monoclinic angle b). In an isothermal run at 135 K the reversible orthorhombic T d to monoclinic 1T 0 transition is observed at E0.8 GPa (E0.4 GPa) at pressure increase (decrease) (Fig. 4c). Thus, application of P well below 1 GPa decreases the temperature of structural transition to below 135 K. Furthermore, at PE1.5 GPa, the 1T 0 structure remains stable down to at least 80 K. The quantitative discrepancy in the T s values derived from structural and resistivity data is most likely due to nonhydrostatic pressure conditions in the resistivity measurements, and the thermal hysteresis since the resistivity curves are recorded with increasing temperatures.
The stability of MoTe 2 in different phases can be explained using total energy calculations within density-functional theory (DFT). The optimized lattice constants are very close to experimental values for both phases, as shown in Supplementary  Fig. 6 and Supplementary Table 3. After evaluating the total energies of the two phases at ambient pressure, we found that the T d phase exhibits slightly lower energy (0.5 meV per formula unit) than the 1T 0 phase. This is consistent with the fact that the low-and high-T phases are T d and 1T 0 , respectively, without external pressure. As the 1T 0 phase can be obtained by sliding between layers of the T d phase, the former exhibits a slightly smaller equilibrium volume than the latter, as also revealed from the lattice parameters measured via SXRD. As illustrated by the energy-volume profile in Fig. 1d, external pressure will stabilize the 1T 0 phase with the smaller volume (and correspondingly higher density) by increasing the shift between neighbouring layers.
The dome-shaped superconductivity behaviour. Our pressure studies have revealed that the T c is very sensitive to pressure. That is, T c increases dramatically to 5 K at relatively low pressures below 1 GPa, before beginning a slower increase to a maximum T c of 8.2 K at 11.7 GPa (Figs 3b and 5). Beyond this pressure, T c decreases and no superconductivity with T c 41.5 K is found at P434.9 GPa (Fig. 3c). Remarkably, the drastic increase of T c at low pressures is associated with a sharp decrease of the 1T 0 -T d structural phase transition temperature T s . Subsequently at higher pressures, T c still increases to its maximum value with increasing P but with significantly lower rate. Our findings demonstrate that the strong enhancement of T c at relatively low P is associated with suppression of the 1T 0 -T d structural phase transition. All the characteristic temperatures in the above experimental results are summarized in the T-P phase diagram in Fig. 5. A dome-shaped superconducting phase boundary is obtained for MoTe 2 , with a sharp slope towards the zero-P end of the diagram. The bulk character of the superconductivity is confirmed by observations of the magnetic shielding effect in the low pressure range and at 7.5 GPa (Supplementary Fig. 7). The onset temperatures of the diamagnetism are consistent with that of the resistivity drop and confirm the drastic increase of T c in the low pressure range (Fig. 5). Further, we conducted resistivity measurements in the vicinity of T c for various external magnetic fields. As can be seen in Fig. 3d, the zero-resistance-point T c under P ¼ 11.2 GPa is gradually suppressed with increasing field. Deviating from the Werthamer-Helfand-Hohenberg theory based on the single-band model, the upper critical field, H c2 (T), of MoTe 2 has a positive curvature close to T c (H ¼ 0), as shown in Fig. 3e. This is similar to the behaviours of both WTe 2 (ref. 18) and NbSe 2 (ref. 32). The experimental H c2 (T) data can be described within the entire T/T c range by the expression H c2 (T) ¼ H c2 *(1-T/T c ) 1 þ a (refs 18,33). The fitting parameter H c2 * ¼ 4.0 T can be considered as the upper limit for the upper critical field H c2 (0), which yields a Ginzburg-Landau coherence length x GL (0) of B9 nm. The corresponding data obtained at P ¼ 1.1 GPa is also shown in Fig. 3e. It is also worth noting that our estimated value of H c2 (0) is well below the Pauli-Clogston limit.
We repeated the high-pressure experiments using different crystal flakes. Similar superconducting behaviour with almost identical T c was observed. For comparison with 1T 0 -MoTe 2 , we also measured r(T) for the 2H-MoTe 2 single crystal at various pressure values. We found a pressure-induced metallization at 15 GPa (Supplementary Fig. 8), which is consistent with previous theoretical predictions 22 . However, in contrast, we did not detect any signature of superconductivity in the 2H phase for pressures up to 40 GPa.

Discussion
For MoTe 2 , the superconducting behaviour in the low-P region clearly differs from that in the high-P region. Under quite low P, the sharp increase in T c is concomitant with a strong suppression of the structural transition, which is reminiscent of observations for other superconductors with various kinds of competing phase transitions. The drastic increase of the T c occurs within the T d phase, which is shown by DFT calculations to be a Weyl semimetal ( Supplementary Fig. 9a and Supplementary Note 2) with a band structure around the Fermi level, which is extremely sensitive to changes in the lattice constants 24,34 . Thus, one can expect that dramatic structural and electronic instabilities emerge in the low-P region, which may account for the strong enhancement of T c . At higher pressures, the topologically trivial (due to inversion and time reversal symmetry) 1T 0 phase (Supplementary Fig. 9b and Supplementary Note 2) remains stable in the whole temperature range. Although within this phase T c still continues to increase up to its maximum value, the rate of the increase is significantly lower and this growth is naturally explained by the increase of the electronic density of states at the Fermi level in the 1T 0 phase ( Supplementary Fig. 9c). Thorough exploration of superconductivity in MoTe 2 from both experimental and theoretical perspectives is required.

Methods
Single-crystal growth. 1T 0 -MoTe 2 crystals were grown via chemical vapour transport using polycrystalline MoTe 2 powder and TeCl 4 as a transport additive 35 . Molar quantities of Mo (Sigma Aldrich 99.99%) were ground in combination with purified Te pieces (Alfa Aesar 99.99%), pressed into pellets and heated in an evacuated quartz tube at 800°C for 7 days. Crystals were obtained by sealing 1 g of this powder and TeCl 4 (3 mg ml À 1 ) in a quartz ampoule, which was then flushed with Ar, evacuated, sealed and heated in a two-zone furnace. Crystallization was conducted from (T 2 ) 1,000 to (T 1 ) 900°C. The quartz ampoule was then quenched in ice water to yield the high-temperature monoclinic phase. The obtained crystals were silver-gray and rectangular in shape. 2H-MoTe 2 crystals were grown using a similar method, but without quenching.
Structural and transport measurements at ambient pressure. The structures of the MoTe 2 crystals were investigated using SXRD with Mo K a radiation. To analyse the atomic structure of the material, HAADF-STEM was performed. The dependence of the electrical resistivity r on temperature T was measured using a conventional four-probe method (low-frequency alternating current, Physical Property Measurement System (PPMS), Quantum Design). Temperatures down to 0.08 K were achieved using a home-built adiabatic demagnetization stage. The pulsed magnetic field experiments were conducted at the Dresden High Magnetic Field Laboratory (Helmholtz-Zentrum Dresden-Rossendorf, HLD-HZDR).
Experimental details of high-pressure measurements. A non-magnetic diamond anvil cell was used for r measurements under P values of up to 40 GPa. A cubic BN/epoxy mixture was used for the insulating gaskets and Pt foil was employed in the electrical leads. The diameters of the flat working surface of the diamond anvil and the sample chamber were 500 and 200 mm, respectively. The initial sample thickness was E40 mm. Electrical resistivity at zero magnetic field was measured using the dc current in van der Pauw technique in a customary cryogenic setup (lowest achievable temperature 1.5 K). The resistivity values were defined as an average of five successive measurements at constant temperature. Resistivity measurements in magnetic field were performed on PPMS. Pressure was measured using the ruby scale 36 by measuring the luminescence from small chips of ruby placed in contact with the sample.
The high-P Raman spectra were recorded using a customary micro-Raman spectrometer with a HeNe laser as the excitation source and a single-grating spectrograph with 1 cm À 1 resolution. Raman scattering was calibrated using Ne lines with an uncertainty of ±1 cm À 1 .
High-pressure diffraction experiments have been performed at ID09A synchrotron beamline using monochromatic x-ray beam (E ¼ 30 keV, l ¼ 0.413 Å) focused to 15 Â 10 mm 2 on the sample 37 . We used a membrane-driven highpressure cell equipped with Boehler-Almax seats and diamond anvil design, allowing an opening cone of 64°. The culet size was 600 mm and the sample was loaded together with He as pressure transmission medium into a hole in a stainless steel gasket preindented to B80 mm with an initial diameter of 300 mm. Low temperature data were collected in a He-flow cryostat. Single-crystal data have been collected by a vertical-acting o-axis rotation, with an integrated step scan of 0.5°a nd a counting time of 1 s per frame. Diffraction intensities have been recorded with a Mar555 flat-panel detector. Diffraction data have been processed and analysed with CrysAlisPro-171.37.35 and Jana2006 software. Pressures were measured with the ruby fluorescence method 36 .
DFT calculations. DFT calculations were performed using the Vienna Ab-initio Simulation Package with projected augmented wave potential 38,39 . The exchange and correlation energy was considered at the generalized gradient approximation level for the geometry optimization 40 , and the electronic structure was calculated using the hybrid functional (HSE06) 41 . Spin-orbital coupling was included in all calculations. Van der Waals corrections were included via a pair-wise force field of the Grimme method 42 . In the lattice relaxation, the volumes were fixed while lattice constants and atomic positions were optimized. The pressure was derived by fitting the total energy dependence on the volume with the Murnaghan equation 43 . After checking the k convergence, the 24 Â 12 Â 8 and 7 Â 5 Â 3 k-meshes with Gaussian-type smearing were used for the generalized gradient approximation (Supplementary Fig. 10) and HSE06 calculations, respectively. The band structures, density of states and Fermi surfaces were interpolated in a dense k-mesh of 200 Â 200 Â 200 using the maximally localized Wannier functions 44 extracted from HSE06 calculations.