Doping-induced superconductivity in the topological semimetal Mo₅Si₃

In the past decade, topological superconductors (TSC) have received widespread attention as a new quantum state of matter TSCreview1 ; TSCreview2 ; TSCreview3 . The most prominent character of TSC is the existence of Majorana fermions TSCreview1 ; TSCreview2 . These fermions are their own antiparticles and obey non-Abelian statistics, which makes TSC useful in fault-tolerant quantum computing. In theory, in addition to topological materials that are intrinsically superconducting superconductingTM1 ; superconductingTM2 ; superconductingTM3 ; superconductingTM4 , doped topological materials that exhibit superconductivity are also natural candidates for TSC TSCreview3 . In reality, examples in the latter category include $A_{x}$Bi₂Se₃ ($A$ = Cu, Sr, Nb) CuxBi2Se3 ; SrxBi2Se3 ; NbxBi2Se3 , Tl_0.6Bi₂Te₃ TlxBi2Te3 , Sn_1-xIn_xTe Sn1-xInxTe , K- and [C₆H₁₁N₂]-intercalated WTe₂ KxWTe2 ; organicintercalated . These materials are all based on transition metal or main-group chalcogenides, and most of their parent compounds are either topological insulators or topological crystalline insulators. In comparison, doping-induced superconductivity has been rarely observed in topological semimetals. Very recently, CoSi was shown to have a topologically nontrivial band structure CoSi1 ; CoSi2 , suggesting that TSC may also be found in transition metal silicides. However, no such example has been reported to date. Note that, compared with chalcogenides, the transition metal silicides generally have higher hardness and thermal stability highhardness , and thus are better suited for practical applications.

Several theoretical calculations consistently show that Mo₅Si₃ is a high symmetry line topological semimetal Mo5Si3prediction1 ; Mo5Si3prediction2 ; Mo5Si3prediction3 . This material belongs to the tetragonal $D$8_m category of the $A_{5}$$B_{3}$ family, and its structure is sketched in Figs. 1(a) and (b). In the tetragonal unit cell, there are two distinct Mo sites Mo(1) and Mo(2), the nearest-neighbours of which form zigzag and linear chains running along the $c$-axis, respectively Mo5Si3structure . Since the density of states at the Fermi level [$N$($E_{\rm F}$)] of Mo₅Si₃ is dominated by the Mo 4$d$ states, this one-dimensional arrangement of the Mo atoms results in significant anisotropy in physical properties including thermal expansion and resistivity Mo5Si3anisotropy . However, Mo₅Si₃ has long been studied as a high-temperature structural alloy HTalloy1 ; HTalloy2 ; HTalloy3 , while little attention has been paid to its low temperature properties. In this respect, it is worth noting that a number of compounds isostructural to Mo₅Si₃ are found superconducting and their $T_{\rm c}$ correlates with the average number of valence electrons per atom ratio ($e$/$a$) Nb5Sn2Al . The $e$/$a$ value falls in the range between 4.25 and 4.625 for most of these superconductors, but is significant higher (5.25) for W₅Si₃ that is isoelectronic to Mo₅Si₃. This suggests the presence of another superconducting region at higher $e$/$a$ values, which is also expected by the Matthias rule MTrule . It is thus speculated that superconductivity may be induced in Mo₅Si₃ by increasing the number of valence electrons.

With this in mind, we employ Re as a dopant since it has one more valence electron than Mo. Structural analysis indicates that Mo_5-xRe_xSi₃ retains a single tetragonal structure up to $x$ $\approx$ 2, and the increase of Re content $x$ results in a reduction of the $a$-axis but has little affect on the $c$-axis. For $x$ $\geq$ 0.5, bulk superconductivity is observed with a maximal $T_{\rm c}$ of 5.78 K observed at the Re solubility limit. The dependencies of $T_{\rm c}$ on $N$($E_{\rm F}$), electron-phonon coupling constant as well as $e$/$a$ are examined, and various superconducting parameters are obtained. Moreover, the evolution of band topology with Re doping is investigated by theoretical calculations. The implication of these results on the possibility of topological superconductivity in Re-doped Mo₅Si₃ is discussed.

Polycrystalline Mo_5-xRe_xSi₃ samples with $x$ = 0, 0.5, 1, 1.5 and 2 were prepared by the arc melting method. High purity powders of Mo (99.9%), Re (99.9%) and Si (99.99%) were weighed according to the stoichiometric ratio, mixed thoroughly using a mortar and pestle, and pressed into pellets in an argon-filled glovebox. The pellets were melted several times in an arc furnace under argon atmosphere, followed by rapid cooling on a water-chilled copper plate. The resulting ingots were grounded, pressed gain into pellets, and annealed at 1600 ^∘C in a vacuum furnace for 24 hours, followed by furnace cooling to room temperature. We have examined carefully ingots and pellets of all samples but no single crystals could be obtained.

The phase purity was checked by powder x-ray diffraction (XRD) at room temperature using a Bruker D8 Advance diffractometer with Cu K$\alpha$ radiation. The chemical composition was measured with an energy-dispersive x-ray (EDX) spectrometer affiliated to a Hitachi field emission scanning electron microscope (SEM). Electrical resistivity and specific heat measurements were carried out in a Quantum Design Physical Property Measurement System (PPMS-9 Dynacool). The resistivity was measured using a standard four-probe method down to 1.8 K, and, if necessary, then from 1.8 to 150 mK with an adiabatic dilution refrigerator option. The applied current is 1 mA. The specific heat was measured down to 1.8 K using a relaxation method. Magnetic susceptibility measurements down to 1.8 K were performed in a Quantum Design Magnetic Property Measurement System (MPMS3) with an applied magnetic field of 0.5 mT in both zero-field cooling (ZFC) and field cooling (FC) modes. For consistency, all the results were collected on the same sample for each $x$ value.

First-principles band structure calculations were performed using the Perdew-Burke-Ernzerhof (PBE)PBE exchange-correlation functional in the Vienna ab-initio simulation package VASP . Our convergence threshold of Hellmann-Feynman force is 0.01 eV/Å and the energy convergence criteria was set to 10^-6 eV. In both optimization and self-consistent calculations, the energy cutoff was fixed to 450 eV. Besides, we adopted 9$\times$9$\times$9 $k$ points to mesh the Brillouin zone. The effect of spin-orbital coupling (SOC) SOC is included for Wannier-function-based calculations of $Z_{2}$ invariants SOC ; wanier .

Fig. 1(c) shows the results of XRD measurements for the series of Mo_5-xRe_xSi₃ samples. It is obvious that all the patterns are very similar, indicating that the structure remains unchanged upon Re doping. For the refinement, the $I$4/$mcm$ space group is employed and the Re atoms are assumed to occupy disorderly the Mo(1) and Mo(2) sites (see Table I) orderedmodel . As exemplified in Figs. 1(d)-(f), a good agreement is obtained between the calculated and observed patterns (the CIF files are available through the ICSD database, CSD 2027050-2027052) and the refinement results are listed in Table II. For $x$ = 2, a small impurity peak is discernible at 2$\theta$ $\approx$ 43^∘ [see the inset of Fig. 1(f)], suggesting that this $x$ value is very close to the solubility limit of Re in Mo₅Si₃. Figures 2(d)-(f) show the refined lattice parameters and unit-cell volume ($V$) plotted as a function of Re content $x$. The lattice parameters for Mo₅Si₃ ($x$ = 0) are $a$ = 9.648(1) Å and $c$ = 4.903(1) Å, in good agreement with the previous report Mo5Si3structure . With increasing $x$, the $a$-axis decreases by $\sim$1.1 % to 9.545(1) Å, which is clearly evidenced by the shift of (400) peak position toward higher 2$\theta$ values [see the inset of Fig. 1(g)]. In comparison, the variation of $c$-axis is within $\sim$0.2 %. As a result, $V$ shrinks by nearly 2% at $x$ = 2 compared with $x$ = 0, which is as expected since Re has a smaller atomic radius than Mo radius .

The morphology of these Mo_5-xRe_xSi₃ samples was also investigated by SEM. At low $x$ values, the samples contains disconnected grains with a size of several tenth $\mu$m. As the Re content increases, the grains become interconnected with the voids getting fewer and smaller. This signifies a growth in the grain size, probably due to a reduction in the energy barrier caused by Re doping. The EDX spectra were collected from several locations for each sample (see Fig. S1 of the Supporting Information). Averaging the data yields the measured chemical compositions of Mo_5.06(8)Si_2.93(8), Mo_4.54(11)Re_0.47(9)Si_2.99(9), Mo_4.01(11)Re_1.09(3)Si_2.90(12), Mo_3.65(6)Re_1.43(3)Si_2.91(7), and Mo_3.17(13)Re_1.83(6)Si_2.99(11) for $x$ = 0, 0.5, 1, 1.5 and 2, respectively, which agree with the nominal ones within the experimental error.

Figure 2(a) shows the temperature dependence of resistivity ($\rho$) for the series of Mo_5-xRe_xSi₃ samples. In all cases, $\rho$ decreases smoothly with decreasing temperature, indicative of a metallic behavior without any phase transition. For undoped Mo₅Si₃ ($x$ = 0), $\rho$ remains finite down to 150 mK and the residual resistivity ratio (RRR) is about 3. When increasing $x$ to 0.5, while the $\rho_{\rm 300K}$ value remains nearly unchanged, the RRR ratio is reduced to 1.5. With further increasing $x$, the $\rho$($T$) curve shifts up almost rigidly, and the low temperature $\rho$ value for $x$ = 2 is nearly one order of magnitude larger than that for $x$ = 0. This suggests that the incorporation of Re atoms leads to enhanced electron scattering. Despite this enhancement, a clear drop to zero resistivity is observed for all Re-doped samples, and the resistive transition moves to higher temperatures as the increase of Re content. From midpoints of the resistive transitions, the values of $T_{\rm c}$ are determined to be 1.67 K, 4.45 K, 5.29 K, and 5.78 K for $x$ = 0.5, 1, 1.5 and 2, respectively. One may note that, in these samples, a higher $T_{\rm c}$ is correlated with a larger normal-state $\rho$. However, it should be pointed that the resistivity of polycrystalline samples as used in the present study largely depends on the contribution of grain boundaries GB . Thus this correlation needs to be verified when single crystals become available.

The occurrence of superconductivity is corroborated by the magnetic susceptibility ($\chi$) and specific heat ($C_{\rm p}$) results shown in Figs. 2(c) and (d). Large shielding fractions exceeding 100% at 1.8 K (without correction for demagnetization effect due to the irregular sample shapes) and strong $C_{\rm p}$ anomalies are observed for the Mo_5-xRe_xSi₃ samples with $x$ $\geq$ 1, indicating bulk superconductivity. As for $x$ = 0.5, such anomaly is absent since it is expected below the lowest measurement temperature of 1.8 K. The $T_{\rm c}$ values determined from the onset of diamagnetic $\chi$ are 4.63 K, 5.27 K and 5.78 K for $x$ = 1, 1.5 and 2, respectively. On the other hand, entropy conserving constructions of the $C_{\rm p}$ anomalies yield $T_{\rm c}$ = 4.15 K, 5.11 K, 5.66 K, and $\Delta$$C_{\rm p}$/$\gamma$$T_{\rm c}$ = 1.42, 1.48, 1.64 for the same series of samples. Note that the $T_{\rm c}$ values determined from transport and magnetic measurements are close to each other and higher than that determined from the thermodynamic measurements. The difference is less than 0.2 K for $x$ = 1.5 and 2 but attains a significantly larger value of $\sim$0.5 K for $x$ = 1, presumably due to lower sample homogeneity.

For all $x$ values, the normal-state $C_{\rm p}$ data are analyzed by the Debye model

where $\gamma$ and $\beta$ are the Sommerfield and phonon specific heat coefficients, respectively. Then the Debye temperature can be calculated as

where $n$ = 8 and $R$ = 8.314 J mol^-1 K^-1 is the molar gas constant. Thus we obtain $\gamma$ = 24.2 mJ mol^-1 K^-2, 24.1 mJ mol^-1 K^-2, 25.5 mJ mol^-1 K^-2, 28.7 mJ mol^-1 K^-2, 29.8 mJ mol^-1 K^-2, and $\Theta_{\rm D}$ = 407 K, 406 K, 403 K, 397 K, 386 K for $x$ = 0, 0.5, 1, 1.5 and 2, respectively. From $\Theta_{\rm D}$, the electron phonon coupling strength $\lambda_{\rm ep}$ can be estimated using the inverted McMillan formula McMillam ,

where $\mu^{\ast}$ is the Coulomb repulsion pseudopotential. According to Ref. McMillam , $\mu^{\ast}$ is usually between 0.1 and 0.13, the latter of which is taken for all transition metal elements. Since the $N$($E_{\rm F}$) of Mo_5-xRe_xSi₃ are dominated by the contributions from Mo and Re atoms, $\mu^{\ast}$ value of 0.13 is reasonable. Actually, we have checked the possible influence of the variation $\mu^{\ast}$ on the calculated results of $\lambda_{\rm ep}$ and found that it is insignificant. Hence, for convenience, $\mu^{\ast}$ is assumed to be the same for all samples. This gives $\lambda_{\rm ep}$ = 0.46, 0.57, 0.60, and 0.62 for $x$ = 0.5, 1, 1.5 and 2, respectively.

By subtracting the phonon contribution, we obtain the the normalized electronic specific heat $C_{\rm el}$/$\gamma$$T$ for $x$ $\geq$ 1 as shown in Fig. 2(e). In order to fit the data, we employ a modified BCS model, or the so-called $\alpha$ model alphamodel . This model still assumes a fully gapped isotropic $s$-wave pairing while allows a variation of the coupling constant $\alpha$ $\equiv$ $\Delta_{\rm 0}$/$T_{\rm c}$, where $\Delta_{\rm 0}$ is the superconducting gap at 0 K. Note that $\alpha_{\rm BCS}$ = 1.768 in the standard BCS theory BCSthoery . The $C_{\rm el}$/$\gamma$$T$ data for $x$ = 1.5 and 2 can be well reproduced by the model with $\alpha$ = $\alpha_{\rm BCS}$ and 1.88, respectively. In comparison, the agreement with the data and the model with $\alpha$ = $\alpha_{\rm BCS}$ is slightly worse for $x$ = 1. This is probably due to the sample inhomogeneity as noted above. Nevertheless, it is emphasized that the overall quality of the fitting is well comparable to that reported in the literature HCfit . In addition, the $\alpha$ value for $x$ = 2 is larger than that for $x$ = 1 and 1.5, which is consistent with the trend of increasing $\lambda_{\rm ep}$ with Re content. Taken together, these results suggest that the Mo_5-xRe_xSi₃ are weak coupling superconductors with a fully isotropic gap.

Figures 3(a)-(c) show the temperature dependence of resistivity under various magnetic fields for the Mo_5-xRe_xSi₃ samples with $x$ = 1, 1.5 and 2, respectively. Increasing the field leads to a gradual suppression of the resistive transition, and the same 50%$\rho_{\rm N}$ criterion is used to determine $T_{\rm c}$ under field. The resulting upper critical field ($B_{\rm c2}$)-temperature phase diagrams are summarized in Fig. 3(d). As can be seen, the $B_{\rm c2}$($T$) data for $x$ = 1 are well fitted by the Werthamer-Helfand-Hohenberg (WHH) model WHH , yielding a zero-temperature upper critical field $B_{\rm c2}$(0) = 4.4 T. In contrast, the data for the other two samples show upward deviation from the WHH behavior especially at low temperature. As such, the $B_{\rm c2}$(0) values are estimated by extrapolating with the Ginzburg-Landau (GL) model

where $t$ = $T$/$T_{\rm c}$. This gives $B_{\rm c2}$(0) = 6.5 T and 8.5 T for $x$ = 1.5 and 2, respectively. With these $B_{\rm c2}$(0) values, the GL coherence length $\xi_{\rm GL}$ can be calculated by the equation

where $\Phi_{0}$ = 2.07 $\times$ 10^-15 Wb is the flux quantum. Hence $\xi_{\rm GL}$ values of 8.7 nm, 7.1 nm and 6.2 nm are obtained for $x$ = 1, 1.5 and 2, respectively.

Now we examine the correlation between $T_{\rm c}$ and the physical parameters $\gamma$ and $\lambda_{\rm ep}$ to gain some insight into the pairing mechanism of Mo_5-xRe_xSi₃. As can be seen from Figs. 4(a) and (b), $T_{\rm c}$ tends to increase with the increases of both $\gamma$ and $\lambda_{\rm ep}$, which is consistent with the BCS theory BCSthoery . However, the $\gamma$ value is nearly the same for $x$ = 0 and 0.5, and hence the emergence of superconductivity is unlikely due to a change in $N$($E_{\rm F}$). Indeed, when increasing $x$ from 0.5 to 2, $T_{\rm c}$ is enhanced by more than a factor of 3, while $\gamma$ is increased by only $\sim$24 %. Remarkably, $T_{\rm c}$ of Mo_5-xRe_xSi₃ exhibits a linear dependence on $\lambda_{\rm ep}$, suggests that it is primarily governed by the electron-phonon coupling strength. Previous study shows that superconductivity emerges in the isostructural compound Mo₅Ge₃ after neutron irradiation, which dose not modify its $\gamma$ but results in phonon softening Mo5Ge3 . According to McMillan McMillam ,

where $N$(0) is the bare density of states at the Fermi level, $M$ is the atomic mass, $\langle$$I^{2}$$\rangle$ and $\langle$$\omega^{2}$$\rangle$ are the averaged electron-phonon matrix elements and phonon frequencies, respectively. For irradiated Mo₅Ge₃, $\lambda_{\rm ep}$ is enhanced mainly due to the decrease of $\langle$$\omega^{2}$$\rangle$ since $\Theta_{\rm D}$ reduces significantly from 377 K to 320 K after irradiation Mo5Ge3 . In contrast, the values of $N$(0), $M$ and $\langle$$\omega^{2}$$\rangle$ are nearly the same for the Mo_5-xRe_xSi₃ samples with $x$ = 0 and 0.5. Thus the increase in $\lambda_{\rm ep}$ in this case can only be due to the enhancement of electron-phonon matrix elements. It is thus clear that the effect of Re doping is different from that of irradiation in inducing superconductivity. In this respect, the phonon spectrum as well as its evolution with Re doping in Mo_5-xRe_xSi₃ is definitely of interest for further investigations.

Figure 4(c) shows the $T_{\rm c}$ dependence on $e$/$a$ for Mo_5-xRe_xSi₃ together with previously known isostructural superconductors Nb5Sn2Al . According to the Matthias rule, $T_{\rm c}$ of intermetallic superconductors is expected to exhibit two maxima at $e$/$a$ close to 4.7 and 6.5 MTrule . Indeed, the $e$/$a$ values for most of the superconductors isostructural to Mo_5-xRe_xSi₃ are in the range of 4.25-4.625 with a maximum $T_{\rm c}$ of 5 K observed at $e$/$a$ = 4.6. As for Mo_5-xRe_xSi₃, the $e$/$a$ values of 5.312-5.5 fall significantly above this range and $T_{c}$ shows a rapid increase with increasing $e$/$a$, which is consistent with the presence of another $T_{\rm c}$ maximum at higher $e$/$a$. In this regard, a higher $T_{\rm c}$ might be expected by substituting Mo in Mo₅Si₃ with elements that can supply more valence electrons than Re, such as Ru, Rh, Pd, Os, Ir, and Pt. On the other hand, this can serve as a useful guide for the search of superconductivity in related $A_{5}$$B_{3}$ compounds, such as Mo₅Ge₃ Mo5Ge3 , Cr₅Si₃ Cr5Si3 , Cr₅Ge₃ Cr5Ge3 , which may significantly enlarge this family of superconductors.

Since Mo₅Si₃ is predicted to be a topological semimetal, it is of natural interest to investigate the evolution of band topology with Re doping. Fig. 5(a) shows the Brillouin zone of Mo_5-xRe_xSi₃, and, as can be seen, there are five high symmetry points, $\Gamma$, Z, M, X and P. The calculated band structure with SOC included for Mo₅Si₃ ($x$ = 0) is depicted in Fig. 5(b). The result indicates that several bands are crossing the Fermi level ($E_{\rm F}$), consistent with the metallic nature. Without considering SOC, there are two nodal lines: one is surrounding M point at Z-M-$\Gamma$ plane and another one is the X-P high symmetry line. When turning on SOC, two gapped Dirac points are located at $\sim$0.45 eV below the $E_{\rm F}$ and the two protected Dirac points are located exactly a the X and P points. This opens a gap between the valence and conduction bands (see the green region). Therefore, we can still calculate the four $Z_{2}$ invariants ($\nu_{0}$;$\nu_{1}$, $\nu_{2}$, $\nu_{3}$) to be (0;111), indicating that the undoped system is in the weak topological insulator (TI) phase. Note that the fourfold degeneracy of bands at X/P point is protected by various symmetries (mirror $M_{z}$, inversion and time-reversal symmetries) even under SOC. This, together with the nontrivial topological index, demonstrates that Mo₅Si₃ is a Dirac nodal line semimetal, confirming the previous studies Mo5Si3prediction1 ; Mo5Si3prediction2 ; Mo5Si3prediction3 .

As indicated by above XRD results, the Re dopants are distributed homogeneously in the lattice and hence the point group symmetries remain unchanged. In view of this, virtual crystal approximation have been adopted to elucidate the band structure variation induced by Re doping. Figs. 5(c) and (d) show the band structures without considering SOC for $x$ = 0 and 0.5, respectively. A comparison of these two plots uncovers that the bands near $E_{\rm F}$ for $x$ = 0.5 look very similar to those near $E$ $-$ $E_{\rm F}$ = $-$0.6 eV for $x$ = 0. This indicates that the band character and band ordering of Mo_5-xRe_xSi₃ with $x$ $>$ 0 resemble closely the valence bands of undoped Mo₅Si₃ so that $Z_{2}$ invariants of the former can be facilely checked. As also seen in Fig. 5(b), the $Z_{2}$ invariants are (1;000) when $E$ $-$ $E_{\rm F}$ ranges from $-$0.25 eV to $-$1.5 eV and (1;111) when $E$ $-$ $E_{\rm F}$ ranges from $-$1.5 eV to $-$2.0 eV. Clearly, this indicates that the Re-doped Mo₅Si₃ are mostly in the strong TI phase, though the band topology changes with the Re doping level. In passing, we have also calculated the density of states as a function of energy for Mo_5-xRe_xSi₃ (see Fig. S2 of the Supporting Information). The evolution of calculated $N$($E_{\rm F}$) with Re content is consistent with that from the $C_{\rm p}$ results.

From above results, one can see that doped silicides Mo_5-xRe_xSi₃ with 0.5 $\leq$ $x$ $\leq$ 2 not only exhibit fully gapped superconductivity, but also possess non-trivial band topology characterized by strong $Z_{2}$ invariants. These together render them promising candidates for TSC TSCreview1 ; TSCreview2 ; TSCreview3 . In this regard, future angle resolved photoemission spectroscopy and scanning tunneling microscopy studies are called for to probe the band structure and superconducting gap directly. In particular, it is of significant interest to see whether zero-bias conductance peaks can be found within the magnetic vortex cores for certain $x$ values, which is a hallmark of the existence of Majorana bound states ZBCP1 ; ZBCP2 ; ZBCP3 . Also, thin film growth of these silicides is worth pursuing. On one hand, by choosing proper substrates, a compressive or tensile strain could be generated, which may increase $\lambda_{\rm ep}$ and hence enhance $T_{\rm c}$. On the other hand, electrostatic gating of these films can be used to tune the $E_{\rm F}$ continuously. This would allow us to control both $T_{\rm c}$ and band topology, and may find applications in Si-based superconducting devices.

In summary, we have discovered Re-doping induced superconductivity in the topological semimetal Mo₅Si₃. The substitution of Re for Mo results in a shrinkage of the Mo_5-xRe_xSi₃ unit cell along the $a$-axis up to the solubility limit of $x$ $\approx$ 2. Meanwhile, fully gapped superconductivity is observed for 0.5 $\leq$ $x$ $\leq$ 2 and $T_{\rm c}$ increases monotonically with the Re content. At $x$ = 2, $T_{\rm c}$ reaches a maximum of 5.87 K, which is the highest among superconductors of this structural type. Our analysis shows that the emergence of superconductivity as well as the trend in $T_{\rm c}$ is mainly attributed to the enhancement of electron-phonon coupling. In addition, $T_{\rm c}$ is found to increase as the increase of $e$/$a$, implying that a higher $T_{\rm c}$ may be achieved by adding more valence electrons. First-principles calculations show that Re doping turns the system into strong TI phase, which is characterized by $Z_{2}$ invariants (1;000) or (1;111) depending on the doping level. The combination of a fully gapped superconducting state and nontrivial band topology makes Mo_5-xRe_xSi₃ a promising candidate for TSC. Our study suggests that transition metal silicides may offer a new playground to explore topological superconductivity, which might facilitate the creation and control of Majorana fermions in silicon-based devices.

We acknowledge financial support by the foundation of Westlake University. The work at Zhejiang University is supported by National Key Research Development Program of China (No.2017YFA0303002), National Natural Science Foundation of China (No.11974307, No.61574123), Zhejiang Provincial Natural Science Foundation (D19A040001), Research Funds for the Central Universities and the 2DMOST, Shenzhen Univeristy (Grant No.2018028).