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# Quantum spin Hall state in monolayer 1T'-WTe2

## Abstract

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling1,2. By investigating the electronic structure of epitaxially grown monolayer 1T'-WTe2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulk bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T'-WTe2 as a new class of QSH insulator with large bandgap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).

## Main

A two-dimensional (2D) topological insulator (TI), or a quantum spin Hall insulator, is characterized by an insulating bulk and a conductive helical edge state, in which carriers with different spins counter-propagate to realize a geometry-independent edge conductance 2e2/h (refs 1,2). The only scattering channel for such helical edge current is back scattering, which is prohibited by time reversal symmetry, making QSH insulators a promising material candidate for spintronic and other applications.

The prediction of the QSH effect in HgTe quantum wells sparked intense research efforts to realize the QSH state3,4,5,6,7,8,9,10,11. So far only a handful of QSH systems have been fabricated, mostly limited to quantum well structures of three-dimensional (3D) semiconductors such as HgTe/CdTe (ref. 3) and InAs/GaSb (ref. 6). Edge conduction consistent with a QSH state has been observed3,6,12. However, the behaviour under a magnetic field, where time reversal symmetry is broken, cannot be explained within our current understanding of the QSH effect13,14. There have been continued efforts to predict and investigate other material systems to further advance the understanding of this novel quantum phenomenon5,7,8,9,15. So far, it has been difficult to make a robust 2D material with a QSH state, a platform needed for widespread study and application. The small bandgaps exhibited by many candidate systems, as well as their vulnerability to strain, chemical adsorption, and element substitution, make them impractical for advanced spectroscopic studies or applications. For example, a QSH insulator candidate stanene, a monolayer analogue of graphene for tin, grown on Bi2Se3 becomes topologically trivial due to the modification of its band structure by the underlying substrate11,16. Free-standing Bi film with 2D bonding on a cleaved surface has shown edge conduction9, but its topological nature is still debated17. It takes 3D out-of-plane bonding with the substrate and large strain (up to 18%) to open a bulk energy gap in monolayer bismuth15. Such 3D bonding structure may induce similar surface issues as seen in 3D semiconductor QSH systems. Monolayer FeSe grown on a SrTiO3 substrate has also emerged as a model system to support both QSH and superconductivity. However, due to doping from the substrate, the Fermi energy (EF) is more than 500 meV higher than the non-trivial gap, making it less practical for applications18.

1T′ phase monolayer TMDCs MX2, M = (W, Mo) and X = (Te, Se, S), are theoretically predicted to be a promising new class of QSH insulators with large bandgap10. Among them, WTe2 is the only one for which the 1T′ phase is most energetically favoured. Realization of a QSH insulator in 2D TMDCs would be a breakthrough as this is a robust family of materials with none of the complications from surface/interface dangling bonds that are seen in 3D semiconductors, enabling a broad range of study and application of QSH physics. In this work, we report a successful growth of monolayer 1T′-WTe2 using molecular beam epitaxy (MBE) on a bilayer graphene (BLG) substrate. In-situ ARPES measurements clearly show the band inversion and the opening of a 55 meV bulk bandgap, which is an order of magnitude larger than gaps seen in quantum wells of 3D semiconductors3,6. Scanning tunnelling spectroscopy (STS) spectra show evidence of the insulating bulk and conductive edge nature of 1T′-WTe2. Our results thus provide compelling experimental evidence of a QSH insulator phase in monolayer 1T′-WTe2.

Figure 1a presents the crystal structure of monolayer 1T′-WTe2. MX2 has three typical phases, namely 2H, 1T and 1T′. 1T-WTe2 is composed of three hexagonally packed atomic layers in an ABC stacking. The metal atoms are in octahedral coordination with the chalcogen atoms. This is not a stable phase in free-standing form and undergoes a spontaneous lattice distortion into the 1T′ phase via a doubling of the periodicity in the X direction. W atoms are dislocated from the original octahedral positions to form a zigzag chain in the Y direction.

The lattice distortion from the 1T phase to the 1T′ phase induces band inversion and causes 1T′-WTe2 to become topologically non-trivial10,19,20. Figure 1b schematically summarizes this topological phase transition in 1T′-WTe2. Without spin–orbit coupling (SOC), the inverted bands cross at a momentum point along the Γ–Y direction, forming a Dirac cone. Strong SOC lifts the degeneracy at the Dirac point, opening a bulk bandgap. Following the bulk-boundary correspondence21,22, the helical edge state is guaranteed by the gapped topologically non-trivial bulk band structure.

Our first-principles band structure calculations for 1T- and 1T′-WTe2 are presented in Fig. 1c–e, which is generally consistent with the literature10,20,23. The key bands for the band inversion with opposite parities are marked to track their evolution. In 1T-WTe2, the bands from 5dxz and $5{d}_{{z}^{2}}$ orbitals of W are separated by the EF (Fig. 1c). Due to the symmetry breaking through the lattice distortion from 1T to 1T′, these orbitals hybridize substantially. Figure 1d shows that the ${d}_{{z}^{2}}$ orbital is lowered below EF whereas the dxz orbital lifts in the opposite direction near the Γ point. Because these two inverted bands have different parities at the Γ point, the Z2 invariant v, in which (-1)v determined by the product of all occupied band parity eigenvalues24, changes from 0 to 1. The valence band maximum in the 1T′ phase is mainly from the W dyz orbital, with an even parity at the Γ point. When its degeneracy with the dxz orbital in the 1T phase is lifted by the lattice distortion, the band stays below EF and does not involve in the band inversion. With the inclusion of SOC (Fig. 1e), the bands further hybridize with each other and the degeneracies at the Dirac cones formed by the band inversion are lifted, opening a bandgap in the bulk states. We note here that different calculation methods give different estimates on the size of the bandgap for strain-free 1T′-WTe2 monolayers. The generalized-gradient approximation (Perdew–Burke–Ernzerhof, PBE) usually underestimates the bandgap and gives a negative bandgap value10, while PBE with hybrid function (HSE06) gives a positive value23.

Figure 2 summarizes the MBE growth and the characterization of 1T′-WTe2 on BLG/SiC(0001) (see Methods for the details of the growth condition). The reflection high-energy electron diffraction (RHEED) pattern of the BLG substrate and the monolayer 1T′-WTe2 are presented in Fig. 2a. Clean vertical line profiles after the deposition of W and Te clearly indicate the layer-by-layer growth mode. Using the lattice constant of BLG (a = 2.46 Å) as a reference, the lattice constant of the grown film is estimated to be 6.3 Å ± 0.2 Å, consistent with the expected value for monolayer 1T′-WTe2 (ref. 23). The angle-integrated core level photoemission spectrum (Fig. 2b) exhibits the characteristic peaks of W and Te for the 1T′ phase. Two differently coordinated types of Te contribute two sets of Te 4d peaks, while the clean doublet feature of the W 4f peaks indicates a pure 1T′ phase rather than a mixed phase of 1T′ and 1H (ref. 25). Figure 2c is an atomically resolved scanning tunnelling microscopy (STM) image of 1T′-WTe2, from which a 7.5° angle distortion is observed, which is universal in bulk 1T′ phase MX2 (refs 25,26). Supplementary Fig. 5a, b show a typical morphology of the 1T′-WTe2 on BLG substrate. A typical diameter for a branched island is 50 nm, with branches having sizes larger than 20 nm × 20 nm. Since the growth is edge-diffusion limited, the edge geometry is random.

The measured Fermi surface (FS) from the in-situ ARPES is shown in Fig. 2e. Due to the symmetry mismatch between the two-fold rotational symmetry of the sample and the three-fold symmetry of the substrate, there exist three energetically equivalent domains rotated by 120° with respect to each other, and each domain contributes two electron pockets along the Γ–Y direction of their respective Brillouin zones27. The experimental band dispersion along Γ–Y cutting the FS electron pockets is inevitably superposed with the contributions from Γ–P and Γ–P’. However, as shown in Fig. 2f–h, the valence bands from Γ–P’ and Γ–P directions are enclosed by the Γ–Y band. Therefore, the existence of multiple domains does not affect the characterization of the gap size and the separation between valence and conduction bands. Overall band structure measured with ARPES (Fig. 2f, g) gives a nice agreement with the HSE06 calculation (Fig. 2g), demonstrating the 1T′ nature and the high quality of our thin-film samples. The predicted band inversion in 1T′-WTe2 is well established experimentally by a polarization-dependent ARPES measurement, from which one can clearly distinguish in- and out-of-plane orbital characters and their inversion around the Γ point (Supplementary Figs 1 and 2). This indicates the non-trivial topology of 1T′-WTe2.

The signature of strong SOC in 1T′-WTe2 is the lifting of state degeneracy at the Dirac cones along the Γ–Y direction, resulting in an opening of the bulk gap as illustrated in Fig. 3a. This can be seen more clearly in the energy distribution curves (EDCs) extracted at the valence band top and the conduction band bottom. Since the ARPES data in Fig. 2 show only faint tails of the bulk conduction band, we deposited potassium (K) onto the surface to raise EF (ref. 28) and make the conduction band more clearly visible to ARPES. Figure 3b focuses only on the low-energy electronic structure of surface K-doped 1T′-WTe2, with EF raised 70 meV to reveal the conduction band bottom more clearly. The corresponding EDCs in Fig. 3c show that the conduction band and the valence band are well separated from each other. To quantify the size of the bandgap, we extracted two EDCs from the momentum positions at the conduction band bottom and valence band top, labelled by the dashed lines in Fig. 3b, and overlaid them in Fig. 3d. The red and green peaks in Fig. 3d correspond to the energy positions of the conduction band bottom and the valence band top, respectively. We estimate the size of the bandgap to be 55 ± 20 meV and 45 ± 20 meV in intrinsic and K-doped samples, respectively (Supplementary Fig. 3). This is in clear contrast to the bulk 1T′-WTe2, which is a semimetal with a complex band structure near EF exhibiting multiple Fermi pockets29. The stacking of energy momentum dispersions with fine momentum steps parallel to the Γ–Y direction (Fig. 3e, f) further establish the effect of SOC by showing that the gap never closes for any momentum across the FS.

Now that we have established band inversion and the opening of a bandgap due to the strong SOC, the remaining signature of a QSH insulator is the conductive edge state in contrast to the insulating bulk, which can be better examined by STS. Figure 4a shows the local differential conductance (dI/dV) spectrum taken at a point far away from the WTe2 edges, which represents the bulk local density of states (LDOS). The peak positions in dI/dV are in good agreement with the band edges found in ARPES. The agreement between ARPES and STS further extends to the size of the gap, as the mean gap size determined by STS is 56 ± 14 meV (Supplementary Fig. 6). In contrast to the gap in the bulk, dI/dV at a 1T′-WTe2 edge is very different, showing a ‘V-shape’ spectrum with states filling in the bulk gap (Fig. 4b), which may indicate the existence of a conductive edge state. Indeed, similar dI/dV spectral line shapes have been reported for other topological systems with distinct edge states15,30 and have been attributed to the one-dimensional (1D) nature of the edge states and the emergence of a Luttinger liquid15. Figure 4c shows dI/dV as a function of energy and distance away from an edge, which demonstrates that the V-shaped conductance is localized at the edge of the WTe2. We observe that such localized edge states run continuously along our sample edges (Supplementary Fig. 7), with only small variations in the fine details of the spectra, regardless of the size, shape, and edge roughness of samples. This provides evidence of the edge state’s topologically non-trivial nature30,31.

By combining ARPES and STS results, we provide strong evidence supporting the direct observation of all the characteristic electronic properties of a QSH state with a large energy gap in 1T′-WTe2, confirming the theoretical prediction10. Such a robust platform for a QSH insulator in 2D TMDCs should provide new opportunities for fundamental studies and novel device applications. Since TMDCs are inert, widely available, can be exfoliated for transport experiments, and be made into few-layer and van der Waals heterostructure devices, we expect them to be the material of choice for a much expanded, multimodal effort to understand and utilize QSH systems.

## Methods

### Thin-film growth.

The monolayer 1T′-WTe2 films were grown by MBE on bilayer graphene (BLG) epitaxially grown on 6H-SiC32. Growth was performed at Beamline 10.0.1, Advanced Light Source, Lawrence Berkeley National Laboratory. The base pressure of the MBE chamber was 4 × 10−10 torr. Ultrahigh-purity tellurium (99.999%) and tungsten (99.999%) was evaporated from an effusion cell and an electron beam evaporator, respectively. The flux ratio between tungsten and tellurium is set between 1:10 1:20. We found that the quality of the sample does not depend much on the ratio. However, it depends critically on the substrate temperature. The substrate temperature was held at 280 °C during growth. The growth process was monitored by RHEED. The growth rate was 40 min per monolayer. After growth we annealed the sample at 300 °C for 2 h to improve the film quality33.

### ARPES measurement.

In-situ ARPES measurements were performed at Beamline 10.0.1, Advanced Light Source, Lawrence Berkeley National Laboratory. ARPES data were acquired with a Scienta R4000 electron analyser at a temperature of 60 K. The energy and angular resolutions are set to be 18 meV and 0.1°, respectively. Two different photon polarizations were used. In the S-polarization, the electric field of the photon is perpendicular to the incidence plane defined by the sample normal and the photon momentum. In the P-polarization, the photon electric field is 10° out of the incidence plane. It is composed of both s polarized and p polarized light. The intensity ratio between the s polarization and p polarization is 17:83. We nonetheless refer to this as P-polarization, since the actual polarization is dominated by p polarized light. The spot size of the photon beam on the sample was 100 μm × 100 μm. The potassium used to perform a surface doping of the film was evaporated from a SAES Getters alkali metal dispenser.

### STM measurement.

To protect the film from an exposure to air during the transfer to the STM chamber, Te and Se capping layers with thicknesses of 100 nm were both deposited on the film (Te layer first) before taking the samples out of the ultrahigh-vacuum (UHV) system of Beamline 10.0.1. Annealing at 200 °C for half an hour was enough to remove the capping layer immediately before STM measurements after having introduced the sample into the STM UHV system. Scanning tunnelling spectroscopy (STS) measurements were performed at T = 4.8 K with platinum iridium tips calibrated against the Au(111) Shockley surface state. dI/dV measurements were obtained via lock-in detection of the a.c. tunnelling current induced by a 5 mV, 613.7 Hz modulation voltage applied to the STM tip.

### Electronic structure calculations.

The band structure and orbital content as presented in Fig. 1 are calculated using the full-potential linearized augmented plane wave method implemented in Wien2k. Ab initio calculations were performed in the framework of the Perdew–Burke–Ernzerhof (PBE) type generalized-gradient approximation (GGA) of density functional theory (DFT). The band structure calculations as presented in Figs 2g, h and 3a in the main text were calculated using the VASP package with projector augmented wave pseudo-potentials, using the Heyd–Scuseria–Ernzerhof (HSE06) exchange–correlation functional with spin–orbital coupling (SOC). The lattice constants and internal atom positions are optimized with the PBE exchange–correlation functional10.

### Data availability.

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

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 FA9550-14-1-0277 through the University of Washington that support 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, US DOE under Contract No. DE-AC02-05CH11231. SSRL is supported by the Office of Basic Energy Sciences, US DOE under Contract No. DE-AC02-76SF00515. Scanned probe measurements were supported by the VdW Heterostructure Program (KCWF16) (STM spectroscopy) funded by the Office of Basic Energy Sciences, US DOE under Contract No. DE-AC02-05CH11231, as well as by National Science Foundation award EFMA-1542741 (surface treatment and topographic characterization). Z.L. is supported by the National Natural Science Foundation of China (11227902). S.T. acknowledges support by the CPSF-CAS Joint Foundation for Excellent Postdoctoral Fellows. J.J. and C.-C.H. acknowledge the support of the NRF, Korea (No. 2011-0030787 and No. 2017R1A2B2003928). 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). M.M.U. acknowledges financial support from Spanish MINECO Grant No. MAT2014-60996-R. A portion of the computational work was performed using the resources of the National Energy Research Scientific Computing Center (NERSC) supported by the US Department of Energy, Office of Science, under Contract No. DE-AC02-05CH11231.

## Author information

Authors

### Contributions

S.T., C.Z., S.-K.M. and Z.-X.S. proposed and designed the research. S.T. performed the MBE growth. S.T. and C.Z. carried out the ARPES measurements and analysed the ARPES data with help from J.J., H.R., S.-K.M., M.H. and D.L. D.W., Z.P., H.-Z.T., S.K., M.M.U. and M.F.C. performed the STM measurements and analysed STM data. C.J., M.C., B.M. and T.P.D. carried out the density functional calculations and provided theoretical support. S.T., S.-K.M., D.W. and Z.-X.S. wrote the manuscript with contributions and comments from all authors.

### Corresponding authors

Correspondence to Sung-Kwan Mo or Zhi-Xun Shen.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 1482 kb)

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Tang, S., Zhang, C., Wong, D. et al. Quantum spin Hall state in monolayer 1T'-WTe2. Nature Phys 13, 683–687 (2017). https://doi.org/10.1038/nphys4174

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