Topological materials have provided an important platform for exploring new physics and realizing novel quantum phenomena.^[1,2] For example, quantum spin Hall effect (QSHE)^[3–5] is expected in two-dimensional topological insulators.^[6] Transition metal dichalcogenides (TMDCs) with distorted trigonal structure ( ) have been predicted to be important candidates for realizing QSHE with potential applications in topological field effect transistors.^[7–11] Recently, -WTe₂ thin films have been revealed to show electronic properties compatible with QSHE.^[12–14] -MoTe₂ has similar crystal structure to -WTe₂^[15] and can also be a potential candidate for QSHE. MoTe₂ crystalizes in three structures, hexagonal (2H), monoclinic ( ),^[15] and orthorhombic (T_d).^[16] Bulk single crystal of -MoTe₂ undergoes a phase transition to phase^[16] which hosts type-II Weyl fermions,^{[ ? ,17,19]} and a superconducting transition has been reported at even lower temperature,^[20] however, mechanically exfoliated few layered -MoTe₂ has been reported to be a semiconductor.^[15]

While growth of -MoTe₂ thin film by chemical vapor deposition has been reported,^[21–25] molecular beam epitaxy (MBE) growth of -MoTe₂ films under ultra-high vacuum has the advantage of being directly compatible with the in situ electronic structure measurement by angle-resolved photoemission spectroscopy (ARPES). So far, despite extensive efforts, molecular beam epitaxy growth of atomically thin -MoTe₂ films^[26–29] has been challenging due to the existence of another stable phase 2H-MoTe₂,^[30] which often leads to a mixture of both and 2H phases in the as-grown MoTe₂ films.^[26–28] Here we report the successful growth of -MoTe₂ films at the optimum growth condition after a systematic study of the film growth at different substrate temperatures. ARPES measurements show that the as-grown film shows a metallic behavior with an overlap between the conduction and valence bands. First principles calculation suggests that a 3% tensile uniaxial strain along the a-axis direction is needed to induce a significant gap to be compatible with QSHE.

The -MoTe₂ films were grown on bilayer graphene/6H-SiC(0001) by MBE. The 6H-SiC(0001) substrate was degassed at 650 °C and annealed from 650 °C to 1350 °C for 60 cycles to form bilayer graphene films on the top surface.^[31] High purity Mo (99.99% purity) and Te (99.999% purity) were then evaporated through an e-beam evaporator and Knudsen cell respectively with a flux ratio of ∼1:20. The growth process was monitored by in situ reflection high energy electron diffraction (RHEED) and low energy electron diffraction (LEED). ARPES measurements were performed in situ with a helium lamp source at a temperature of ∼10 K under ultra-high vacuum.

The density functional theory (DFT) calculations are performed using the Vienna ab initio simulation package (VASP)^[32] with the Perdew–Burke–Ernzerhof (PBE)^[33] exchange–correlation functional and a plane wave energy cut-off of 500 eV. A k-point grid of 16 ×20 ×1 is applied to sample the Brillouin zone. The pristine geometric structure of the monolayer is fully relaxed until the residual forces on each atom are less than 0.001 eV/Å, and the obtained equilibrium lattice parameters are a = 3.475 Å and b = 6.367 Å. To simulate the uniaxial strain along the a-axis (b-axis), a stain is applied along the a-axis (b-axis), and the length of b-axis (a-axis) as well as the ionic positions is optimized until the residual forces are less than 0.001 eV/Å. The spin–orbit coupling (SOC) effect has been taken into account in our calculations.

Figure 1(a) and 1(b) show the top and side views of the crystal structure of -MoTe₂. The Mo atoms deviate from the center of the octahedron formed by six Te atoms, forming zigzag Mo chains along the a-axis direction (see the top view in Fig. 1(a)) and distorted Te octahedra in the b–c plane (side view in Fig. 1(b)). Graphene is a fantastic substrate for growing films with different crystal structures and symmetries through van der Waals epitaxiy,^[34] and is used as the substrate for growing -MoTe₂ film. Figure 1(c) and 1(d) show the RHEED and LEED patterns of the graphene/SiC substrate. Figure 1(e) and 1(f) show the RHEED and LEED patterns of the -MoTe₂ films under optimum growth conditions. Sharp streaky stripes (indicated by yellow arrow in Fig. 1(e)) and six diffraction spots (Fig. 1(f)) from the -MoTe₂ film are observed in the RHEED and LEED patterns, respectively. The -MoTe₂ film grows mainly along the same orientation as the graphene substrate with a small distribution of azimuthal angles in the LEED pattern due to the weak van der Waals growth with weak coupling between the -MoTe₂ film and graphene. Because of the different crystal symmetries between the substrate (three-fold symmetry) and the -MoTe₂ film (two-fold symmetry), there are three equivalent orientations of -MoTe₂ films on graphene, leading to apparently hexagonal LEED patterns, similar to the case of -WTe₂ film^[12] and the previous report on -MoTe₂^[29] yet with better LEED pattern. The observation of diffraction spots from both the -MoTe₂ film and the graphene substrate suggests that the -MoTe₂ film is atomically thin, ∼1 monolayer (ML) thick. Increasing the growth time leads to weaker diffraction spots from the substrate and the graphene diffraction spots disappear at 2 ML (see Appendix A), however, no major change in the electronic structure is observed since the difference in the electronic structure of monolayer, bilayer, and multilayer -MoTe₂ films is small due to the small band splitting. Using the lattice constants of graphene as a reference, the extracted in-plane lattice constants of -MoTe₂ from the LEED pattern are a = 3.47 Å and b = 6.48 Å, suggesting a 2% (tensile) strain along the b-axis direction compared to the lattice constants of a = 3.48 Å and b = 6.33 Å in the bulk crystal.^[15]

Fig. 1.

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Fig. 1. Crystal structure of -MoTe2 and diffraction patterns from RHEED and LEED. (a) and (b) Top and side views of the crystal structure of -MoTe2. Red and green balls represent Te and Mo atoms, respectively. The dashed box indicates the unit cell. RHEED patterns of (c) the graphene/SiC substrates and (e) the as-grown -MoTe2 sample. LEED patterns of (d) the graphene/SiC substrates and (f) the as-grown -MoTe2 sample measured at a beam energy of 120 eV. The white and yellow arrows indicate the patterns from graphene and -MoTe2, respectively.

The growth condition is critically dependent on the substrate temperature. Figure 2 shows a systematic study of the RHEED and LEED patterns of the films grown at different substrate temperatures while maintaining other experimental conditions fixed. When the substrate temperature is 331 °C, no detectable signals from MoTe₂ are observed in the RHEED (Fig. 2(a)) or LEED patterns (Fig. 2(e)). Only in a small temperature window of ∼ 25°C between 338 °C and 363 °C, streaky stripes can be observed (indicated by the yellow arrows) in RHEED (Figs. 2(b)–2(d)) and diffraction spots are observed in the LEED patterns (Figs. 2(f)–2(h)). The sharpest streaky stripes from the RHEED pattern (Fig. 2(c)) and the best signal from the LEED pattern (Fig. 2(g)) obtained at the substrate temperature of 350 °C indicate that the optimum growth condition includes the substrate temperature of 350 °C.

Fig. 2.

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	Fig. 2. RHEED and LEED patterns for films grown at different substrate temperatures. (a)–(d) RHEED patterns after growing at the substrate temperature of 331 °C, 338 °C, 350 °C, and 363 °C, respectively. (e)–(h) Corresponding LEED patterns. The yellow and white arrows indicate diffraction spots from -MoTe2 and graphene, respectively.

Although bulk crystal of -MoTe₂ is quite stable in air, atomically thin -MoTe₂ films have been reported to be very sensitive to air.^{[23,26,30,35,36]} Therefore ex situ atomic force microscopy (AFM) and Raman characterizations of the films are not practical. Direct experimental electronic structure of the as-grown film by in situ ARPES measurements can provide direct evidence for the -MoTe₂ film, and moreover, provide insights for evaluating its compatability with QSHE.

Figure 3 shows the electronic structure of -MoTe₂ revealed by in situ ARPES measurements. Figure 3(a) shows the intensity maps measured from E_F to −0.84 eV. Since the 2H-MoTe₂ is a semiconductor with a gap of larger than 1 eV,^[37] this confirms that the measured band dispersion is not from the 2H-MoTe₂ but from the -MoTe₂. A hexagonal pocket centered at the point is observed at E_F and its size increases at low energies, suggesting that it is a hole pocket. Below −0.56 eV, a new pocket emerges at the Γ point and further splits into two circular pockets, resulting in three hole pockets in total at −0.84 eV. Figure 3(b) shows the dispersions measured along the –X direction. The dispersion shows a linear dispersing hole pocket through E_F and two parabolic bands below −0.56 eV, consistent with the intensity maps in Fig. 3(a). Figure 3(c) shows a zoom-in of the dispersion near E_F. In addition to the hole pocket near E_F as discussed above, there is another dispersing band within −0.15 eV, suggesting that this is likely the electron pocket from the conduction band. Figure 3(d) and 3(e) show the calculated band dispersion for comparison.^[12] By using the extracted experimental lattice constant from LEED, which indicates a strain of 2% (tensile) along the b-axis direction, a good agreement with the experimental results is obtained. The overall band structure is similar to that of -WTe₂,^[12,38] yet with two major differences. Firstly, the two bands below −0.56 eV almost cross (pointed by the red arrow in Fig. 3(b)), which is different from those in the -WTe₂ film and is not discussed in previous work on -MoTe₂.^[12] Indeed, the better agreement between the ARPES data and the calculated band structure of the strained film compared to the calculated result of the unstrained film in previous work^[12] also indicates the important role of stain in this material. Secondly, both the experimental and calculated results reveal an overlap between the conduction and valence bands, while doped -WTe₂ has been reported to be an insulator with a gap of 45 meV.^[12] Therefore, our ARPES data and calculation show that different from -WTe₂, the as-grown -MoTe₂ film is metallic with an overlap between the valence and conduction bands.

Fig. 3.

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Fig. 3. Electronic structure of -MoTe2 revealed by ARPES measured at ∼10 K. (a) Intensity maps measured from EF to −0.84 eV with an integrated energy window of 50 meV. (b) ARPES spectrum measured along the –X direction (marked by dotted line in (a)). (c) Zoom-in dispersion near EF. (d) Calculated dispersions along the –X direction (blue) and –P/ (red) and (e) zoom-in dispersion near EF with a uniaxial strain of 2% along the b-axis direction and a shift −0.09 eV in energy.

Since the electronic structures of -MoTe₂ films^[7] and bulk crystals^[39–41] are strongly dependent on the strain, we calculate the evolution of the electronic structure with uniaxial strain to provide more insights. Figure 4 shows the calculated band structure of monolayer -MoTe₂ film under uniaxial strain along the b-axis (Figs. 4(a)–4(e)) and a-axis (Figs. 4(f)–4(j)) with strains ranging from −2% to 3%. The application of a tensile strain along the a-axis direction has similar effect to the application of a compressive strain along the b-axis direction. The uniaxial strain has two major effects. Firstly, it changes the splitting of the two bands below −0.5 eV at the point. More importantly, it changes the energy position of these valence bands significantly, while maintaining the energy position of the conduction band. By applying a tensile strain along the a-axis, the overlap between the valence and conduction bands decreases, until eventually a gap of 47 meV emerges at 3% strain (Fig. 4(j)). The opening of such a band gap is critical, since it makes -MoTe₂ potentially a quantum spin Hall insulator if the Fermi energy is further tuned to inside the gap region. Therefore in order to realize QSHE in -MoTe₂ films, a tensile strain (3%) along the a-axis is needed.

Fig. 4.

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	Fig. 4. Evolution of the electronic structure with strain from first principles calculation. (a)–(e) Calculated band structure of monolayer -MoTe2 with uniaxial strains from −2% to 3% along the b-axis direction. (f)–(j) Calculated band structure of monolayer -MoTe2 with uniaxial strains from −2% to 3% along the a-axis direction. All calculated dispersions are shifted by −0.09 eV in energy.

To summarize, we have successfully grown high-quality atomically thin -MoTe₂ films using MBE after a systematic investigation of the growth at different substrate temperatures, which is confirmed by RHEED, LEED, and ARPES measurements. Furthermore, ARPES measurements show that the as-grown film is a metal with an overlap between the conduction and valence bands, which is attributed to the strain effect. Comparison of calculated band structures at different strains further suggests that a suitable tensile strain (3% tensile strain along the a-axis direction) can induce a significant gap between the conduction and valence bands. Our work not only reports the MBE growth conditions for obtaining -MoTe₂ thin film and its experimental electronic structure, but also provides insights for band structure engineering of -MoTe₂ film to make it a quantum spin Hall insulator.