Nontrivial superconductivity in topological MoTe_2−xS_x crystals

Significance

Searching for topological superconductors is of paramount importance in condensed-matter physics and materials science today: these materials are expected to harbor Majorana fermions on the edge states, an essential component for topological quantum computation platform. We experimentally observed s₊₋ pairing two-gap superconductivity and type-II Weyl semimetal property in T_d-phase MoTe_2−xS_x (x ≈ 0.2). Further, an enhanced surface superconducting gap comparing to bulk gaps is discovered. Our findings are strongly suggestive of topological superconductivity of the T_d-phase MoTe_2−xS_x. This work not only presents an important breakthrough in searching for topological superconductors but also inspires further investigations on the sign-change superconductivity beyond Fe-based high-T_c superconductors.

Abstract

Topological Weyl semimetals (TWSs) with pairs of Weyl points and topologically protected Fermi arc states have broadened the classification of topological phases and provide superior platform for study of topological superconductivity. Here we report the nontrivial superconductivity and topological features of sulfur-doped T_d-phase MoTe₂ with enhanced T_c compared with type-II TWS MoTe₂. It is found that T_d-phase S-doped MoTe₂ (MoTe_2−xS_x, x ∼ 0.2) is a two-band s-wave bulk superconductor (∼0.13 meV and 0.26 meV), where the superconducting behavior can be explained by the s₊₋ pairing model. Further, measurements of the quasi-particle interference (QPI) patterns and a comparison with band-structure calculations reveal the existence of Fermi arcs in MoTe_2−xS_x. More interestingly, a relatively large superconducting gap (∼1.7 meV) is detected by scanning tunneling spectroscopy on the sample surface, showing a hint of topological nontrivial superconductivity based on the pairing of Fermi arc surface states. Our work demonstrates that the T_d-phase MoTe_2−xS_x is not only a promising topological superconductor candidate but also a unique material for study of s₊₋ superconductivity.

Topological Dirac semimetals (TDSs) and topological Weyl semimetals (TWSs) have been shown to host the condensed-matter physics counterpart of relativistic fermions in quantum-field theory (1, 2). Their low-energy quasi-particle states with linear dispersion can be effectively described by the Dirac equation and the Weyl equation, respectively. They are also characterized by nontrivial topological invariants, broadening the classification of topological phases of condensed matter beyond topological insulators (3–13). In contrast to relativistic fermions which need to respect Lorentz invariance, the less constrained condensed-matter systems feature some excitations that have no analogy in high-energy physics. One of the most fascinating quasi-particles in this context exists in type-II TWSs whose Weyl cones are strongly tilted (14–16). In contrast to the point-like bulk Fermi surfaces formed in type-I TDSs and TWSs, these type-II TWSs harbor a finite density of states at the Fermi level.

Topological materials that host superconductivity are ideal systems to detect topological superconductivity and Majorana fermions (17–23). In time-reversal symmetric Weyl semimetals, theory predicts that time-reversal symmetric topological superconductivity can arise from sign-changing superconductivity in Fermi surfaces with different Chern numbers (20). In addition, the superconductivity of topological surface states in TWSs may offer a new opportunity to study topological superconductivity (21) beyond the proximity-effect–induced superconducting surface states of topological insulators.

Other than being a type-II TWS with four pair of Weyl points (WPs) and Fermi arcs (24–30), T_d-MoTe₂ as a transition metal dichalcogenide material is found to be superconducting around 0.1 K (31). Understanding the superconductivity and topological properties of T_d-MoTe₂ is important for elucidating and exploiting topological superconductivity. However, the ultralow T_c has limited the widespread study of superconductivity in T_d-MoTe₂. Recent studies of MoTe₂ have reported dome-shaped curves of T_c vs. pressure and T_c vs. sulfur concentration (31, 32). High-pressure studies of T_d-MoTe₂ suggest the possibility of emergence of a topological s₊₋ superconducting order parameter (33), although it is challenging to fully detect the topological properties in such high-pressure measurements. Here, we report a systematic study of superconductivity and topological properties of MoTe_2−xS_x (x ∼ 0.2 in this paper), wherein the T_c is significantly enhanced to 1.27 K. According to our detailed transport and specific heat experiments, MoTe_2−xS_x is a two-band s-wave bulk superconductor. Our results indicate possible s₊₋ rather than conventional s-wave superconductivity in this material as the interband coupling is stronger than the intraband coupling. By scanning tunneling spectroscopy (STS), we observed quasi-particle interference (QPI) patterns that are consistent with the existence of Fermi arcs. Further calculations reveal that MoTe_2−xS_x is a type-II TWS with Fermi arcs and four pairs of WPs at 5 meV (W1) and 50 meV (W2), respectively. The surface superconducting gap (Δ) found by STS is 1.70 meV at 0.4 K, which is much larger than bulk superconducting gaps and gives a huge gap to critical temperature ratio (at least 8.6) comparing to the conventional BCS (Bardeen–Cooper–Schrieffer) ratio of 1.76, thus suggesting a signature of unconventional superconductivity. In topological systems with s-wave bulk superconductivity, the topological surface states can form odd parity superconductivity (18). The relatively large superconducting gap detected by STS here hints nontrivial superconductivity from the topological surface states.

Results

Two-Band Superconductivity Detected by Magnetotransport Measurements.

MoTe₂ crystallizes in the 1T′ phase (monoclinic, P2₁/m) at room temperature and transitions into the T_d phase (orthorhombic, Pmn2₁) at low temperature. We synthesized MoTe_2−xS_x single crystals by the chemical vapor transport method and characterized them using optical microscopy, cross-sectional scanning transmission electron microscopy (STEM), X-ray diffraction, and scanning tunneling microscopy (STM). In Fig. 1A, the atomically resolved high-angle annular dark-field (HAADF) STEM image manifests the high-quality nature of our MoTe_2−xS_x single crystal, showing the same atomic structure as intrinsic MoTe₂ (31). Fig. 1B is the (001) surface topography scanned by STM under 4.2 K. We carried out a series of transport experiments that mapped out the resistivity of our samples under various temperatures and magnetic fields using a standard four-probe method in a 16T-Physical Property Measurement System (PPMS) from Quantum Design. The current was applied along the Mo chains (a axis) (Fig. 1C). SI Appendix, Fig. S5 shows the typical temperature dependence of the four-probe resistivity from 300 K down to 10 K under zero magnetic field. Around 189 K, there is a peak in the first-order differentiation of the ρ(T) curve, indicating the structural transition from the 1T′ phase to the T_d phase (SI Appendix, Fig. S5A). Compared with undoped MoTe₂, the structural transition temperature is lowered to 189 K from 250 K by doping and the resistivity anomaly hysteresis between cooling down and warming up measurements is weaker (31). The zero-resistivity superconductivity transition temperature T_c = 1.27 K is obtained by extrapolating the superconductivity transition curve (Fig. 1D). We define the onset superconductivity transition temperature, T_c^onset = 2.3 K, at which ρ(T) diverges from its extrapolated normal state (Fig. 1D). T_c^middle = 1.57 K is determined at the temperature where the resistivity drop reaches 50% of ρ_n. ρ_n is the resistivity taken at 4 K without an external magnetic field.

Fig. 1.

Characterization of MoTe_2−xS_x and schematic structure for electrical transport measurements. (A) A high-resolution HAADF-STEM image of MoTe_2−xS_x single crystal taken along the (100) zone axis. The gray spheres simulate the atoms. (B) STM image of cleaved (001) surface of MoTe_2−xS_x, showing atomically resolved lattice. The surface unit cell is indicted by black arrows with lattice constant of a = 3.5 Å and b = 6.3 Å. (C) Schematic structure for electrical transport measurements in MoTe_2−xS_x. (D) Typical resistivity–temperature curve of MoTe_2−xS_x showing superconductivity.

To explore the superconductivity nature of MoTe_2−xS_x, we conducted systematic magnetotransport measurements under a perpendicular field H^⊥ (along the c axis) at different temperatures (Fig. 2A). The upper critical field (H_c2) is defined as the value at which the resistivity drop reaches 50% of ρ_n. The temperature dependence of H_c2^⊥ is shown in Fig. 2B. At 0.5 K, the parallel critical field H_c2^∥ (which is 21.7 kOe along b axis, SI Appendix, Fig. S6) is 6.6 times of the H_c2^⊥(3.3 kOe). This is a typical characteristic of layered superconductors. Both H_c2^⊥ and H_c2^∥ are below the Pauli limit field ${\mathrm{H}}_{\mathrm{p}}\mathrm{(0)}=\mathrm{1}\mathrm{.86}{\mathrm{T}}_{\mathrm{c}}^{\mathrm{middle}}=29.2\hspace{0.17em}\mathrm{kOe}$.

Fig. 2.

Superconducting properties of MoTe_2−xS_x in low-temperature regime. (A) Magnetoresistance at various temperatures under perpendicular field. (B) Temperature dependence of H_c2^⊥. The pink curve and red curve are the best fit of single-band s-wave WHH model and two-band s-wave model to the experimental data, respectively. (C) Magnetization behavior measured under a 3-Oe magnetic field parallel to the (001) sample surface, showing the Meissner effect. (D) Temperature dependence of specific heat divided by temperature C/T for MoTe_2−xS_x single crystal in zero field. The red line represents the best fit to C/T = γ_n + βT². (E) The entropy in the normal and superconducting states as a function of temperature. (F) The electronic specific heat C_es/T as a function of temperature. The red line represents the fit of C_es/T below T_c using the two-band s-wave model.

Interestingly, there is a slight upturn of the critical magnetic field near T_c. Furthermore, when the temperature approaches 80 mK, the observed H_c2^⊥ is enhanced compared with the standard single-band s-wave Werthamer–Helfand–Hohenberg (WHH) model (34) as shown by the pink line in Fig. 2B. This enhancement of H_c2^⊥ at low temperature implies that the two-band effect is not negligible (35). The two-band superconducting behavior has been observed in MgB₂ and Fe-based superconductors. Taking the orbital pair-breaking effect into account and ignoring the interband scattering, H_c2 (T) can be expressed by ref. 35.

$$\begin{array}{l}{\text{a}}_0\left[\ln \hspace{0.17em}t+\text{U}\left(\text{h}\right)\right]\left[\ln \hspace{0.17em}t+\text{U}\left(\mathrm{\eta }\text{h}\right)\right]+{\text{a}}_2\left[\ln \hspace{0.17em}t+\text{U}\left(\mathrm{\eta }\text{h}\right)\right]+{\text{a}}_1\left[\ln \hspace{0.17em}t+\text{U}\left(\text{h}\right)\right]=0\\ \text{t}=\frac{\text{T}}{{\mathrm{T}}_{\text{c}}},\text{U}\left(\text{x}\right)=\mathrm{\psi }\left(\frac{1}{2}+\text{x}\right)-\mathrm{\psi }\left(\text{x}\right)\\ \hspace{0.17em}\mathrm{\eta }=\frac{{\text{D}}_2}{{\text{D}}_1};\hspace{0.17em}\text{h}=\frac{{\text{H}}_{\mathrm{c2}}{\text{D}}_1}{2{\phi }_0\text{T}};\hspace{0.17em}{\text{a}}_0=\frac{2\varpi }{{\mathrm{\lambda }}_0};\hspace{0.17em}{\text{a}}_1=1+\frac{{\mathrm{\lambda }}_{-}}{{\mathrm{\lambda }}_0};{\text{a}}_2=1-\frac{{\mathrm{\lambda }}_{-}}{{\mathrm{\lambda }}_0}\\ \varpi ={\mathrm{\lambda }}_{11}{\mathrm{\lambda }}_{22}-{\mathrm{\lambda }}_{12}{\mathrm{\lambda }}_{21};{\mathrm{\lambda }}_0={\left({\mathrm{\lambda }}_{-}^2+4{\mathrm{\lambda }}_{12}{\mathrm{\lambda }}_{21}\right)}^{\mathrm{1/2}};{\mathrm{\lambda }}_{-}={\mathrm{\lambda }}_{11}-{\mathrm{\lambda }}_{22}.\end{array}$$ [1]

ψ(x) is the digamma function. D₁ and D₂ are intraband diffusivities of bands 1 and 2, and ${\phi }_{\mathrm{0}}$ is the magnetic flux quantum. The parameters a₀, a₁, and a₂ are constants described with intraband and interband coupling strength. Terms ${\mathrm{\lambda }}_{11}$ and ${\mathrm{\lambda }}_{22}$ are the intraband couplings in bands 1 and 2. ${\mathrm{\lambda }}_{12}$ and ${\mathrm{\lambda }}_{21}$ describe the interband couplings between bands 1 and 2. This expression of H_c2 is derived from the Eliashberg equation in which the microscopic details of different bands are described by the normal-state electronic diffusivity tensors D_m for each Fermi surface sheet. The diffusivity ratio $\mathrm{\eta }$ determines the curvature of H_c2(T) curve. We note that when $\mathrm{\eta }=1$, this equation will be reduced to the simplified single-band WHH model. Here, D₂ equals 141D₁, which suggests a significant difference in the electron mobility in the two bands of MoTe_2−xS_x. The red line in Fig. 2B shows a fit of the experimental data with Eq. 1. The fitting parameters are λ₁₁ = 9.7, λ₁₂ = 2.6, λ₂₁ = 2.6, λ₂₂ = 0.5, D₁ = 0.076, D₂ = 10.7, C = 1.015, ϖ = −1.91.

Two-Band s-Wave Bulk Superconductivity Confirmed by Diamagnetism and Specific Heat Measurements.

We obtain additional insights using magnetization measurements of the diamagnetism in the crystals using a Quantum Design Magnetic Property Measurement System (MPMS 7-XL SQUID), with a resolution of 10⁻⁸ EMU. Fig. 2C shows the dc magnetization curves as a function of temperature during zero-field cooling and field cooling under H^∥ = 3 Oe. An apparent drop appears below 1.27 K, indicating the superconducting Meissner effect below T_c.

To further study the superconducting behavior of our sample, we also conducted specific heat measurements in PPMS. Fig. 2D displays the C(T)/T curves of the MoTe_2−xS_x single crystal down to 0.1 K at zero field. We observe a clear anomaly corresponding to the superconducting transition around 1.27 K, consistent with the T_c observed in diamagnetic measurements (Fig. 2C) and transport measurements (Fig. 1D). The normal-state specific heat can be described by C(T) = C_e(T) + C_lattice(T) with electronic contribution of C_e(T) = γ_nT and the phonon contribution of C_lattice(T) = βT³. The red line in Fig. 2D is the best fit to the C/T, yielding γ_n = 2.49 mJ·mol⁻¹⋅K⁻² and β = 1.35 mJ·mol⁻¹⋅K⁻⁴ and a residual value γ_r = 0.2 mJ·mol⁻¹⋅K⁻² (SI Appendix, Fig. S8). And, the superconducting volume ratio is 92% [(γ_n − γ_r)/γ_n ∼ 92%], which manifests the bulk superconductivity of MoTe_2−xS_x. With the normal-state electronic specific heat derived from this fit, the entropy in the normal and superconducting states agrees with (${\displaystyle {\int }_0^{{\mathrm{T}}_{\text{c}}}\left({\mathrm{C}}_{\mathrm{e}}/\text{T}\right)\text{dT}={\mathrm{\gamma }}_{\text{n}}{\mathrm{T}}_{\mathrm{c}}}$) within 1% deviation near the superconducting transition, for which the entropy conservation is confirmed to be satisfied in Fig. 2E. Considering the existence of γ_r, the electronic specific heat for one mole of superconducting material can be defined as ${\mathrm{C}}_{\mathrm{es}}=({\mathrm{C}}_{\mathrm{e}}-{\mathrm{\gamma }}_{\mathrm{n}}\mathrm{T}){\mathrm{\gamma }}_{\mathrm{n}}/({\mathrm{\gamma }}_{\mathrm{n}}-{\mathrm{\gamma }}_{\mathrm{r}})$. Here in MoTe_2−xS_x, the C_es(T)/T can be fitted very well using a two-band s-wave superconductivity model ${\mathrm{C}}_{\mathrm{es}}/\mathrm{T}\propto p{\mathrm{e}}^{\left(-{\mathrm{\Delta }}_1\right)/{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}+(1-p){\mathrm{e}}^{\left(-{\mathrm{\Delta }}_2\right)/{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}$, in which ${\mathrm{\Delta }}_{\mathrm{i}}$ is the superconducting gap and p is a fitting parameter representing the weight of the total electron density of states for each band. Fig. 2F shows that the data are well described by this model with fitting parameter p = 0.3 [the gap values at zero temperature are ${\mathrm{\Delta }}_1=1.22{\mathrm{k}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{c}}$ (0.13 meV) and ${\mathrm{\Delta }}_2=2.42{\mathrm{k}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{c}}$ (0.26 meV)]. This is consistent with the theoretical constraints that one gap must be larger than the BCS gap and one smaller in a weakly coupled two-band superconductor, as observed in MgB₂. Note that muon spin rotation experiments show that the values of the gaps in our MoTe_2−xS_x are almost the same as those of MoTe₂ under 0.45 GPa high pressure (33).

Calculations of Band Structure.

As shown above, our transport, diamagnetism, and specific heat measurements demonstrate two-band s-wave bulk superconductivity in MoTe_2−xS_x. To explore the topological property of MoTe_2−xS_x, we examined its band structure and surface states (Fermi arcs) with x = 0.2 by first-principles calculation. As detailed in Materials and Methods, tight-binding models are obtained to describe the electronic structure of MoTe_2−xS_x and the k-dependent surface spectral function by an iterative projection procedure (36). The Fermi surfaces of MoTe_2−xS_x are mainly located in the central region of the surface Brillouin zone (BZ) except for a small electron pocket near the $\overline{{\rm Y}}$ point. Here, we focus on the central region of the BZ which covers all of the bulk WPs. Fig. 3A shows the surface spectral function at Fermi level E_F. Bowtie-shaped hole pockets appear near $\overline{\mathrm{\Gamma }}$, and electron pockets appear along the path $\overline{\mathrm{\Gamma }}-\overline{{\rm X}}$. According to Fig. 3 B and C, the above observed electron and hole pockets touch each other at eight WPs at ∼E_F + 5 meV (W₁) and ∼E_F + 50 meV (W₂), respectively. Topological Fermi arcs (highlighted by red arrows in Fig. 3 B and C) connecting the WPs with opposite chirality, emerges from W₁ point and ends at W₂ point. The Fermi arc roughly spans 5% of the BZ. Additionally, there are trivial surface states (indicated by red arrows in Fig. 3 B and C) which form a closed loop and merge partially with the bulk electron pocket. Clearly, the Fermi surfaces of MoTe_2−xS_x have almost the same features as undoped MoTe₂ with little modulation of WPs’ energies and positions.

Fig. 3.

Calculated Fermi surfaces of MoTe_2−xS_x. (A) Calculated spectral function at E_F (B) Spectral function at 0.005 eV. (C) Spectral function at 0.05 eV. The range of momentum of B and C is marked by the red rectangle in A. The Weyl points and topological Fermi arcs are pointed out in B and C.

QPI Measurements of Fermi Arcs.

To verify the nontrivial electron states of MoTe_2−xS_x, we performed low-temperature STM measurements (Materials and Methods). The topographic image of a cleaved MoTe_2−xS_x crystal shows atomically flat terraces with stripe-like structure along the a axis (Fig. 1B), similar to undoped MoTe₂ (26). We carried out differential conductance (dI/dV) maps (with spatial resolution at various energies) on such surfaces; this is expected to reveal the QPI patterns generated by surface states. The dI/dV maps are taken within a 50 nm $\times$ 50-nm area at various energies at T = 4.2 K (SI Appendix, Fig. S4). Their corresponding fast Fourier transforms (FFT) are shown in Fig. 4 A–F. One can clearly see the dumbbell-like scattering patterns in these FFT images, similar to that obtained on undoped MoTe₂ (26) and Mo_1−xW_xTe₂ (37).

Fig. 4.

Quasi-particle interference patterns of MoTe_2−xS_x. (A–F) The Fourier transform of the dI/dV maps taken at various energies. The Bragg points $\left(2\pi /b,0\right)$ are indicated by white arrows. (G–L) Calculated JDOS (simulation of QPI) at different energies with respect to E_F. The dumbbell-like patterns are the main feature of Fermi arcs in experimental QPI patterns and calculation results. (M) Sketch of extremal scattering wave vectors between Fermi arcs (q1 and q2) and trivial surface states (q3). (N) Dispersions extracted from QPI by taken line cut along the line marked in A. The calculated dispersions of q1, q2, and q3 are superposed for comparison.

To understand the origin of these patterns, we simulated the QPI by calculating the joint density of states (JDOS):

$$J\left(\mathbf{q},\text{ω}\right)={\displaystyle \sum _{\mathbf{k}}\hspace{0.17em}A\left(\mathbf{k},\text{ω}\right)}A\left(\mathbf{k}+\mathbf{q},\text{ω}\right).$$ [2]

Here, A(k,ω) is the k-dependent surface spectral function and ħω is the energy of the Bloch electron, and the scattering vector q considered here is located only in the first BZ. The calculated JDOS are shown in Fig. 4 G–L. The dumbbell pattern is well reproduced in the simulations. To have a more quantitative comparison, a simplified scattering geometry is sketched in Fig. 4M, in which q1 and q2 connect Fermi arcs and q3 connects trivial surface states. In Fig. 4N, we extracted the dispersion of the dumbbell pattern (by taking FFT profiles along the line marked in Fig. 4A), and the calculated dispersion of q1∼q3 are superposed. We find that the experimental dispersion has a similar trend with q1∼q3, while the strongest scattering weight lies between q1, q3, and q2. This implies the observed scattering is possibly a superposition of q1, q2, and q3. In SI Appendix, Fig. S9C, it is shown that the calculations indicate significant contribution of Fermi arc states to the QPI scattering in the experimental range of bias potential. Thus, the QPI measurements indicate the coexistence of topological Fermi arcs and trivial surface states.

STS Detection of the Superconductivity.

To further study the superconducting state of MoTe_2−xS_x, we performed STS measurement at temperatures below T_c. Fig. 5A is a typical dI/dV spectrum taken at T = 0.4 K on the surface shown in Fig. 1B. We observe a superconducting gap of 1.70 meV; for comparison, there is no gap feature in the STS taken at 4.2 K (see also Fig. 5A). Fig. 5C shows the magnetic field dependence of the STS taken on the same spot. At elevated fields, the gap is gradually filled up and vanishes under a field of 8 kOe, confirming its origin in superconductivity. This critical magnetic field measured by STM is consistent with the value obtained by transport measurements (the onset critical field shown in Fig. 2A). We note that the line shape of the observed gap cannot be fitted well by BCS theory. For comparison, we plot the calculated DOS of an isotropic BCS gap (dashed curve in Fig. 5B) with Δ = 1.7 meV and T_eff = 1.18 K as the broadening factor (effective temperature of our system). The calculated gap significantly differs from the measured spectrum.

Fig. 5.

Superconducting gap on the surface of MoTe_2−xS_x measured by STM. (A) dI/dV spectrum taken on MoTe_2−xS_x sample at 4.2 K (blue curve) and 0.4 K (red curve), respectively. A superconducting gap with Δ = 1.7 meV (as marked) was clearly observed at 0.4 K. (B) Comparison of the measured gap (red curve) with a simulated isotropic BCS gap (dashed curve). (C) dI/dV spectra measured at 0.4 K under various magnetic fields. The gap was obviously suppressed with increasing external magnetic field and the critical magnetic field is 8 kOe.

Discussion

There are two kinds of scenarios for two-band s-wave superconductivity: (i) conventional s-wave pairing dominated by strong intraband coupling $\varpi$ > 0 and (ii) strong interband coupling $\varpi$ < 0 which can result in the π shift between the order parameter on two bands (s₊₋ pairing) (38, 39). Here, in our fitting $\varpi =-1.91$, which supports sign-change superconductivity in MoTe_2−xS_x single crystal, i.e., s₊₋ Cooper pairing. Some Fe-based superconductors (Fe-SCs) have already been predicted and proven to be s₊₋ superconductors. The hole carrier and electron carrier in Fermi surface of Fe-SCs carry the opposite superconducting gap phase. It is believed that spin fluctuations are responsible for the interaction that induces sign-change superconductivity in different Fermi surfaces for Fe-SCs (40, 41). Although hole carriers and electron carriers also coexist in MoTe_2−xS_x, phonons provide the principal interaction for Cooper pairing in MoTe_2−xS_x. This view is supported by the fact that S doping enhances the T_c significantly (32) and that there is no magnetic order in MoTe₂ (33)_. Further, S doping is not supposed to induce magnetic order. Therefore, the origin of the interaction that contributes to the sign-change superconductivity in MoTe_2−xS_x is quite mysterious. Moreover, this kind of sign change of the superconducting gap function between different Fermi surfaces in time-reversal invariant TWS can lead to topological superconductivity.

In addition, the surface superconducting gap size observed by STM (Δ = 1.7 meV) is surprisingly large compared with the T_c of MoTe_2−xS_x. By transport measurements (Fig. 1D), the resistance starts to drop at 2.3 K and reaches zero at 1.27 K. Even if we take 2.3 K as the onset T_c, the BCS ratio (Δ/k_BT_c) is 8.6. This value is much larger than that of the conventional weak-coupling superconductors (1.76), and also larger than the fitting results from our specific heat measurement (1.22 and 2.42). Besides, the line shape of this gap cannot be fitted well by BCS theory. One possible explanation of the unexpected large gap is that it may stem from the topological surface states of MoTe_2−xS_x. It was predicted that in a superconducting topological system with bulk s-wave pairing, a superconducting gap enhancement can occur on the surface states by anomalous parity mixing (18). Intriguingly, recent experiments have shown an enhanced superconducting gap associated with the surface states of β-Bi₂Pd films (The surface superconducting gap is 2.15 meV, while the bulk superconducting gap is 1 meV.) (42). Thus, we speculate that the observed large gap may be related to the Fermi arc surface states of MoTe_2−xS_x. Further experimental and theoretical studies are still needed to clarify its origin.

Conclusion

In summary, we report the discovery of nontrivial superconductivity and topological behavior in T_d phase MoTe_2−xS_x single crystals. Our transport and specific heat measurements show potential s₊₋-wave two-band superconductivity arising from a dominant interband coupling. The s₊₋ paring of TWS MoTe_2−xS_x makes the material a topological superconductor candidate. Moreover, the observed QPI patterns of Fermi arcs are consistent with the calculated nontrivial band structure. In addition, we have detected a relatively large superconducting gap on the sample surface, potentially indicating odd pairing superconductivity from Fermi arc surface states. This kind of s-wave bulk superconductor with Fermi arcs provides a unique platform to investigate topological superconductivity. More interestingly, the weak interlayer van der Waals coupling in this material makes it attractive for potential applications of TWS and superconductor devices.

Materials and Methods

Crystal Growth.

The growth of MoTe_2−xS_x single crystals used for this study has been previously reported (32). Using iodine as the transport agent, 1T′ single crystals of MoTe_2−xS_x were grown by vapor transport method and then quenched in ice water to yield the high-temperature monoclinic phase. First, stoichiometric amounts of Mo, Te, and S were ground and pressed into pellets and then heated in an evacuated quartz tube at 810 °C for 7 d to get polycrystalline MoTe_2−xS_x powder. Then, the powder was sealed in a evacuated quartz tube flushed by Ar and heated with I₂ in a two-zone furnace with the hot zone kept at 1,010 °C and cold zone kept at 910 °C. The single crystal is characterized by various methods as shown in the main text. The concentration of S in single crystal samples is decided by energy-dispersive spectroscopy.

Electronic Structure Calculation.

Density-functional theory calculations were performed using the projector-augmented wave method as implemented in the Vienna ab initio simulation package (VASP) (43) within the generalized gradient approximation parametrized by Perdew, Burke, and Ernzerhof. The energy cutoff is set to 450 eV for a plane-wave basis and the k-point mesh is taken as 12 $\times$ 6 $\times$ 3 for the bulk calculations. The spin-orbit coupling effect is self-consistently included. To calculate the surface and bulk electronic structure, we constructed a tight-binding Hamiltonian for both MoTe₂ and MoS₂, where the tight-binding model matrix elements were calculated by projecting onto the Wannier orbitals, which used the VASP2WANNIER90 interface (44). The lattice parameters of MoTe_2−xS_x single crystal are shown in SI Appendix, Text and Fig. S2. We used Mo d orbitals and Te(S) p orbitals to construct Wannier functions without using the maximizing localization procedure. The electronic structure of the samples with finite doping was calculated by a linear interpolation of tight-binding model matrix elements of MoTe₂ and MoS₂. The surface state electronic structure was calculated by the surface Green’s function technique (36).

STM Measurement.

The STM experiment was conducted in a commercial Unisoku 1300 STM system at the temperature of 4.2 K and 0.4 K. MoTe_2−xS_x samples were cleaved in ultrahigh vacuum at 100 K. PtIr tips were used in all measurements after careful treatment on a Au(111) surface. The tunneling spectroscopy (dI/dV) was performed using a standard lock-in technique with modulation frequency f = 915 Hz and typical amplitude ΔV = 1 mV.