Electronic structure of monolayer 1T′-MoTe₂ grown by molecular beam epitaxy Open Access

Two-dimensional (2D) transition metal dichalcogenide (TMDC) is a versatile material platform, in which electrical, optical, and topological properties can be controlled through thickness, strain, field, and other perturbations.^1–4 The most well-studied example is the 2H-MX₂ (M = Mo, W; X = S, Se) semiconductor that makes a transition from indirect bandgap to direct bandgap only in the monolayer,^4,5 with well-pronounced spin-splitting^6,7 and valley degrees of freedom.^8,9 Other structural phases stemming from different stacking orders between transitional metal and chalcogen layers deliver distinct physical properties even with the same constituent atoms.

1T′-MX₂ (M = Mo, W; X = S, Se, Te) has gained particular interest regarding its topological properties. While its three-dimensional bulk form has been explored in terms of type-II Weyl semimetal,^10–13 the monolayer is predicted to host a quantum spin Hall (QSH) insulator.³ A QSH insulator, or a two-dimensional (2D) topological insulator, is a topologically nontrivial quantum state, which is hallmarked by the helical edge state protected by time reversal symmetry and the bulk (as opposed to the edge) bandgap opening due to strong spin-orbit coupling (SOC).^14–16 The resulting transport properties exhibit quantized Hall conductance even in the absence of magnetic field, and spin-polarized edge current is expected to be useful for the spintronic applications. The QSH phase in 1T′ TMDC has been recently realized only in 1T′-WTe₂.^17,18 It is of great interest whether it is possible to realize a QSH state in other 1T′ TMDCs and whether fundamental parameters such as bulk bandgap would be different from those of 1T′-WTe₂.

Many efforts have been devoted to achieve a QSH state in monolayer 1T′-MoTe₂.^3,19–21 From the electronic structure point of view, two critical elements of achieving a QSH state in group VI TMDCs are the band inversion caused by the structural distortion from the 1T phase to 1T′ phase and the 2D bulk bandgap induced by strong SOC.¹⁸ The former has been well established by the previous theoretical calculations.^3,19,20 However, as shown in Table I, the calculated bandgap size varies significantly depending on calculation methods, even to a degree that it is not clear whether 1T′-MoTe₂ is a semiconductor or a semimetal. Optical absorption and transport measurements report a 60 meV bulk gap in few-layer mechanically exfoliated (ME) 1T′-MoTe₂,²⁰ while CVD-grown monolayer 1T′-MoTe₂ shows a metallic transport behavior.²¹ Whether the SOC is strong enough to open a bulk gap is still not very clear. A characterization tool that can directly visualize the band structure and the size of the bandgap, such as angle-resolved photoemission spectroscopy (ARPES),^22,23 would provide a clearer insight on this aspect.

In this letter, we report a successful growth of monolayer 1T′-MoTe₂ on a bilayer graphene (BLG) substrate using molecular beam epitaxy (MBE). The electronic structure of epitaxial 1T′-MoTe₂ has been investigated by in situ ARPES. We found that the SOC indeed breaks the band degeneracy points and separates the valence and conduction bands. However, the strength of SOC is not enough to open a 2D bulk bandgap, which makes monolayer 1T′-MoTe₂ on BLG a semimetal.

Both thin film growth and ARPES characterization of 1T′-MoTe₂ were performed at the Beamline 10.0.1, Advanced Light Source, Lawrence Berkeley National Laboratory. 1T′-MoTe₂ was grown by MBE with a base pressure of ∼2 × 10⁻¹⁰ Torr. Mo (99.99% purity) and Te (99.999% purity) were evaporated by an e-beam evaporator and a Knudsen cell, respectively, with the flux ratio of ∼1:20. The substrate was BLG prepared by vacuum graphitization of 6H–SiC(0001).²⁴ The substrate temperature was set at 280 °C for growth. The growth rate was 15 min per layer. Following the growth, a 20-min post-annealing process at the same temperature was performed. Additional ARPES measurements were performed at the Beamline 5-4, Stanford Synchrotron Radiation Lightsource (SSRL), SLAC National Accelerator Laboratory. The band structure calculation is performed by using the generalized gradient approximation method with Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional as implemented in the VASP.²⁵ The lattice constants used are a = 6.38 Å and b = 3.45 Å for 1T′-MoTe₂.

The crystal structure of 1T′-MoTe₂ is illustrated in Fig. 1(a). It can be seen as distorted 1T-MoTe₂, for which Mo atoms are in octahedral coordination with Te atoms. With the distortion, Mo atoms shift off the center of Te octahedra along X direction forming zigzag metal chains along the Y direction. The Te atoms also shift accordingly, making two types of Te with inequivalent coordinations. Figure 1(b) shows the Brillion zone of 1T′-MoTe₂. The reflection high-energy electron diffraction (RHEED) patterns before and after the thin film growth are shown in Fig. 1(c). The sharp diffraction stripes after growth indicate the high crystalline quality of the 1T′-MoTe₂ thin film. The thermal stability of the sample was checked by annealing the sample at 350 °C under Te atmosphere. No obvious change in the RHEED pattern was observed, indicating that growth temperature 280 °C is far below the decomposing temperature, thus retaining high crystallinity of the sample.²⁶ Using the lattice constant of BLG ∼2.46 Å as a reference, one can get the lattice parameter of 1T′-MoTe₂ on BLG ∼6.3 Å, which is consistent with reported values.³ Figure 1(d) is the angle-integrated core level spectrum, clearly showing the characteristic Mo 4p peak and Te 4d peaks. Figure 2 is the low-energy electron diffraction (LEED) pattern taken with an electron kinetic energy of 94 eV to reveal the surface symmetry and lattice structure. The blue solid circles indicate the first-order diffraction from a BLG substrate. The six spots surrounding each of them come from $63$R30° superlattice diffractions between graphene and SiC.²⁴ Due to the symmetry mismatch between three-fold rotational symmetric BLG and two-fold symmetric 1T′-MoTe₂, there are three energetically equivalent rotational alignments between BLG and 1T′-MoTe₂.²⁷ This results in three sets of reciprocal lattices superposed in both LEED and ARPES data. The LEED pattern from different domains of 1T′-MoTe₂ is indicated by the dotted lines with different colors in Fig. 2(a). Using the in-plane lattice constant of graphene a = 2.46 Å, one can get the lattice constants of 1T′-MoTe₂, a = 6.3 Å and b = 3.4 Å, consistent with the previously reported values³ as well as with that from our RHEED measurement. Figure 2(b) shows the superposition of the Brillion zones from three equivalent 1T′-MoTe₂ and graphene lattices.

Figure 3 show the overall electronic structure and Fermi surface (FS) topology from ARPES measurements on monolayer 1T′-MoTe₂/BLG. Figure 3(a) is the FS intensity map, which shows six-fold symmetry due to the superposition of three 1T′-MoTe₂ domains with 120° rotation with respect to each other. One may extract a single-domain FS from the ARPES data as shown in Fig. 3(b). There are one hole pocket located at the zone center, two electron pockets along the ΓY direction, and two more electron pockets located at the zone boundaries. The topology of the FS plays a key role in understanding the transport properties of the semimetal in which the hole and electron carriers coexist. Perfect electron-hole compensation is proposed to be responsible for the non-saturating magneto-resistance in three-dimensional bulk 1T′-WTe₂.²⁸ However, too many bands crossing the Fermi energy (E_F) in a confined momentum space have challenged ARPES measurements and interpretations.^29,30 The simplified FS in monolayer 1T′-MoTe₂ makes the evaluation easier and reliable. We have obtained the concentration ratio between the n and p type carriers ∼6:10. Considering that the volume of the electron (hole) pocket increase (decrease) very quickly above E_F, one may easily achieve the balance of n and p carries with slightly doping on the film to realize the electron-hole compensation condition in the monolayer.^1,31

Figure 3(c) is the overall band structure along the ΓY direction measured by in situ ARPES, superimposed with the theoretical calculation made with the PBE method. Due to the superimposed rotational domains, the signal from the ΓP direction [Fig. 1(b)] overlaps with that from the ΓY direction within a single detection plane. However, the low-energy bands from ΓP are contained within the envelop of ΓY bands in both theory and experiment. The domain size of the film is estimated to be tens of nanometers,^1,18 which call for further studies with characterization tools with high spatial resolution such as STM and nano-ARPES to disentangle the superposition of signals from domains with different orientations. Overall, the experimental band structure and FS topology from ARPES agree well with the theoretical calculation.

Now we focus on the low-energy electronic structure right near E_F. According to theoretical calculations,^3,19,20 the transition from 1T to 1T′ inverts the band order leading to a band degeneracy point between the valence and conduction bands at Δ point [Fig. 4(a), left]. The SOC then lifts the degeneracy at the cross point [Fig. 4(a), right] to make the system to be an insulator with a bulk bandgap or a semimetal, depending on the strength of the coupling. The low-energy band dispersion along both ΓX and ΓY directions [Figs. 4(b) and 4(c)] and corresponding momentum distribution curves (MDCs) and energy distribution curves (EDCs) along the ΓY direction [Figs. 4(d) and 4(e)] clearly indicate well-separated valence and conduction bands confirming the scenario mentioned above. However, the band structure measured by ARPES clearly exhibits that the hole band at Γ crosses E_F, while the conduction band minimum locates well below E_F, leading to a FS with both electron and hole pockets. This shows that monolayer 1T′-MoTe₂ on BLG is a semimetal with a moderate strength of SOC.

Considering the weaker SOC in Mo compared to W, in general, one would expect that the SOC-induced energy bandgap in 1T′-MoTe₂ is smaller than that in 1T′-WTe_2. In addition, strain and electron-electron interaction are believed to play important roles in the low-energy electronic structure of 1T′-MoTe₂.^3,32 As shown in the calculations,^3,32 the size of the gap is very sensitive to the lattice constant. However, a large strain, ∼4%–6% of the lattice constant, is needed to lift the crossover of the conduction and valence bands and to open a bulk gap. It has been known that van der Waals epitaxy adopted in our growth of 1T′-MoTe₂ on graphene minimizes the strain effect caused by lattice mismatch.³³ A strong electron-electron correlation, which is largely screened in the bulk 1T′-MoTe₂, could also enlarge the separation between the conduction band and the valence band.³² As calculated in Ref. 32, even with a very strong on-site Coulomb repulsion ∼5 eV, the bandgap remains closed for 1T′-MoTe₂. In our 1T′-MoTe₂/BLG thin films, the screening from conducting graphene substrate lowers the strength of on-site Coulomb interactions, which would act against the bulk gap opening due to the electron-electron interaction.

In summary, high-quality monolayer 1T′-MoTe₂ has been grown on the BLG substrate by MBE. In situ LEED and ARPES measurements are performed to characterize the crystal and electronic structure. It has been shown that three equivalent rotational domains of 1T′-MoTe₂ coexist and contribute to our spectra. The overall electronic structure obtained from ARPES exhibits excellent agreement with theoretical calculations, including the predicted degeneracy lifting induced by SOC. However, the splitting due to the SOC is not large enough to open a 2D bulk gap. The valence band maximum locates above the conduction band minimum resulting in a FS with both electron and hole pockets. Our measurements confirm that the epitaxially grown monolayer 1T′-MoTe₂ on BLG is a semimetal.

The ARPES and thin film growth works at the Stanford Institute for Materials and Energy Sciences and Stanford University are supported by the Office of Basic Energy Sciences, Division of Materials Science and AFOSR Grant No. FA9550-14-1-0277 through the University of Washington that supports the ALS activity by the Stanford team. Research performed at ALS (thin film growth and ARPES) is supported by the Office of Basic Energy Sciences, U.S. DOE under Contract No. DE-AC02-05CH11231. SSRL is supported by the Office of Basic Energy Sciences, U.S. DOE under Contract No. DE-AC02-76SF00515. Z.L. is supported by the National Natural Science Foundation of China (No. 11227902). S.T. acknowledges the support by CPSF-CAS Joint Foundation for Excellent Postdoctoral Fellows. H.R. and C.H. acknowledge the support from the NRF, Korea through Max Planck Korea/POSTECH Research Initiative (No. 2011-0031558) and Basic Science Research Program (No. 2015R1C1A1A01053065). A portion of the computational work was performed using the resources of the National Energy Research Scientific Computing Center (NERSC) supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-05CH11231.