Abstract
Monolayer 1 T′WTe_{2} is a quantum spin Hall insulator with a gapped 2Dbulk and gapless helical edge states persisting to temperatures ~100 K. Despite the farranging interest, the magnitude of the bulk gap, the effect of gating on the 2Dband structure, as well the role interactions are not established. In this work we use STM spectroscopy to measure the intrinsic bulk gap of monolayer 1 T′WTe_{2} and show that gate induced electric fields cause large changes of the gap magnitude. Our firstprinciples DFTderived tightbinding model reveal that a combination of spatial localization of the conduction and valance bands and Rashbalike spinorbit coupling leads to a gating induced spinsplitting of the 2Dbulk bands in the tens of meV, thereby reducing the band gap. Our work explains the large sensitivity of the band structure to electric fields and suggests a new avenue for realizing proximity induced nontrivial superconductivity in monolayer 1 T′WTe_{2}.
Introduction
2D transition metal dichalcogenides present an exciting platform for realizing emergent phases having nontrivial topology and strong correlations, and are prime candidates for hosting topological edge states, topological superconductivity, and fractional excitations^{1}. After more than a decade of intense search, monolayer WTe_{2} (MLWTe_{2}) (Fig. 1a–e) has recently emerged as a 2D timereversal invariant topological insulator, i.e., a quantum spin Hall (QSH) insulator^{2,3,4,5}. While bulk WTe_{2} is a semimetal, band structure calculations of a monolayer indicate that it is a narrowgap semiconductor exhibiting inverted bands that give rise to the QSH phase (Fig. 1f)^{6,7}. Transport studies have confirmed quantized twoterminal edge conductance up to 100 K, and microwave impedance microscopy measurements have been used to observe edge states^{8,9}.
The simplest mechanism to tune the properties of 2D materials is by gating, i.e., the application of an electric field through a dielectric layer. Naively, gating may be expected to add or remove carriers from the film by shifting the bands with respect to the Fermi energy (rigid band shift) as is observed in graphene^{10}. However, gating could have nontrivial effects on the band structure due to the presence of the outofplane electric field, or changes in effective screening. For example, outofplane electric fields break inversion symmetry and can lead to a spin splitting of the bands, like the Rashba effect. In WTe_{2}, electrostatic gating has been used to tune the circular photogalvanic effect^{11} and induce an exotic superconducting phase^{12,13}. Despite the farranging interest in this system and extensive transport studies, the exact gap size of MLWTe_{2}, the dispersion of the edge states within the gap, as well as the effect of gating on the band structure have not yet been established. Indeed, the experimental literature reports a puzzlingly large variation in the observed gap sizes, which has yet to be explained^{2,3,5,7,8,11,12,13,14}. Furthermore, recent studies have suggested that correlation effects may play a critical role in controlling band structure as well as gating dependent effects. Hence, comprehensive gatingdependent spectroscopic data is urgently needed to understand the key elements that control the lowenergy physics of the system, and scanning tunneling microscopy (STM) and spectroscopy (STS) are ideal tools to probe gateinduced effects on the band structure and edge states.
In this work, we present a combined experimentaltheoretical study on MLWTe_{2}. Highquality monolayer WTe_{2} films grown by molecular beam epitaxy (MBE) were studied by STM at 4 K. STM STS reveals clear bulk gaps with edge states that agree with density functional theory (DFT)—Heyd–Scuseria–Ernzerhof (HSE) calculations. We further find that the gap magnitude is highly tunable with gating. This gap tunability is quantitatively explained using a parameterfree firstprinciples DFTderived tightbinding model. The calculations show that the conduction band states are predominantly located on the top and bottom layers with opposite spinmomentum locking, while the valence band states are localized to the interior tungsten layer. Application of an electric field changes the energy spacing between states in the three layers, resulting in a fieldcontrollable spinmomentum selected gap.
Results and discussion
Film structure and topography
Monolayer WTe_{2} has a distorted orthorhombic 1 T′ structure which preserves inversion symmetry (Fig. 1a). Figure 1b shows a large scale STM image of MLWTe_{2} grown on graphene on SiC. These films were transferred directly from the MBE to the STM using a vacuum suitcase (see Methods for details). Multiple monolayer islands of ~20–30 nm size, which correspond to the typical island size of MBEgrown WTe_{2}, can be seen in this field of view. Zooming into a representative island, we can resolve the characteristic stripes corresponding to protruding Te atoms of the top surface (for example, Fig. 1c, d). The observed lattice corresponds well to 1 T′WTe_{2}. A representative bulk spectrum averaged over an area of 5 by 5 nm^{2} on one island (Fig. 1e) exhibits a band gap of approximately 40 meV.
DFT calculations
To compare the experimentally measured gap to standard band theory calculations, we carry out DFT calculations using the Perdew–Burke–Ernzerhof (PBE)^{15} and Heyd–Scuseria–Ernzerhof exchangecorrelation functional (HSE06)^{16} with and without spinorbit interactions to compute the electronic structure of monolayer WTe_{2}. The results are summarized in Fig. 1f. As is common for small gap semiconductors such as Ge, PBE obtains a negative gap, while HSE06 obtains a gap of around 60 meV, within the range of the experimental observations. The bands are inverted due to SOC according to HSE06, and thus we expect the existence of topological helical edge states.
As a benchmark for the topological electronic structure, we identify the bulk and edge states of an island (shown in Fig. 2a) with no applied gate voltage. Upon tracking the spectra from the center of the island to the edge, we observe a bulk insulating gap and an emergence of a finite density of states in the nominal insulating gap as the tip approaches the edge. The ingap density of states arises from the helical edge modes expected for a QSH insulator. The edge modes can be seen more clearly in dI/dV maps shown in Fig. 2d, thus confirming the existence of states which are highly localized to the edge near the Fermi energy, which we assign to be helical QSH edge states. We find that the spatial extent of the edge modes increases as the energy of the modes approaches the bulk band edges. This trend can be seen on both sides of the Fermi energy as plotted in Fig. 2c. This is an expected feature since topological edge modes must eventually merge into the bulk bands at a point beyond which their localization length diverges^{17,18}. In our data, we find that the edge states are maximally localized at the Fermi level and merge into the bulk at the conduction band minima (CBM) and valence band maxima (VBM) values.
Further characterization of the MLWTe_{2} films shows that the bulk gap varies considerably from island to island (Fig. 3b–d). As measured by the difference between the CBM and VBM (E_{g} = E_{cbm}E_{vbm}), the bulk gap can vary between 0 meV and 60 meV for different islands within the same film. The gap is however quite homogeneous within any given island as shown in Supplementary Fig. 3c. This large variation in gap sizes on different islands is not easy to explain, especially since the topographies of areas exhibiting different gaps show no differences in structure or defect concentration. A survey of the literature shows similarly large variations in gap magnitudes between different samples with no consensus on the low temperature gap. A recent study suggests that large strains can lead to gap variations in this system^{19}. However, the samples in that study were deliberately grown to induce strain which is not the case for our samples or other reports. Another possible explanation is that the gap variations arise from trapped ions in the SiC substrate creating local electric fields. Such trapped ions have been previously observed in other films grown on SiC^{20} and could result from the high energy RHEED electrons used to monitor film growth. So, while our measurements substantiate earlier conflicting experimental determinations of the band gap magnitude, the causes of the variations in gap magnitude remain unknown. Using the gatedSTM capability we can systematically investigate the origin of these gap variations by measuring the response of MLWTe_{2} to electric fields.
Effect of gating on band structure
Our gating setup is shown in Fig. 4a where ML WTe_{2} was grown via MBE on chemicalvapordeposited (CVD) graphene transferred onto 300 nm SiO_{2}/Si, with the Si substrate serving as the back gate electrode (see Methods and Supplementary Fig. 1 for details). Figure 4c, d shows a topographical STM image of a representative WTe_{2} island on graphene on SiO_{2}. With this setup, we can apply positive and negative back gate voltages up to a maximum of 80 V. Naively, we expect that the applied electric field would simply modify the carrier concentration resulting in a rigid shift of the Fermi level relative to the bulk bands. The signature of this effect would be a rigid shift of the measured dI/dV spectrum relative to the Fermi energy. As shown in Fig. 4b, we find that gating does indeed move the Fermi energy toward the conduction/valence band consistent with electron/hole doping for positive/negative voltages respectively. However, gating has another, more dominant effect. As shown in Fig. 4b, e, f, with increasing positive gate voltage the band gap increases, while for negative gate voltages the band gap decreases. Hence, we find an inherent sensitivity of the WTe_{2} insulating gap to (even modest) electric fields. At face value, it appears that positive and negative voltages have opposite effects on the gap. However, we will show below that this observed behavior is because the STM signal is dominated by the density of states from the top layer of the sample. In reality, both signs of the gate voltage decrease the net band gap.
Tightbinding model
To gain an understanding of these gatinginduced band structure changes, (see methods section), we fit a tightbinding model to the DFT band structure using Wannier interpolation for our analysis. At zero gate electric field (see second panel of Fig. 5a), the CBM are doubly degenerate at \(k_ \pm \simeq \pm \left( {0.15\frac{{2\pi }}{a},0} \right).\) At \(k_ +\), the spin \(\uparrow\) electron (i.e., the spin pointing in the zdirection) is localized on the top Te atom due to strong spin orbit coupling, while the spin \(\downarrow\) electron is localized on the bottom Te atom. Consistent with timereversal symmetry, this is reversed in the \(k_ \) direction, as noted on the diagram.
Next, we model the applied electric field by adding a term \(\left( {H\prime } \right)\) to the tightbinding model, \(H = H_0 + H^\prime = H_0 + \mathop {\sum }\nolimits_i eE \cdot z_i\), where z_{i} represents the zcoordinate of the ith Wannier center, computed as the expectation value of the position operator on the Wannier function. Figure 5a shows the 2D bulk band structures for different applied gate electric fields, and we see that the electric field breaks the spatial inversion symmetry and spinsplits the doubly degenerate CBM at \(k_ \pm \simeq \pm \left( {0.15\frac{{2{\uppi}}}{a},0} \right)\). The spinsplitting is consistent with preserved timereversal, but broken inversion symmetry. For negative gate voltages the conduction band minimum in the \(k_ +\) direction has spin \(\downarrow\), while the minimum in the \(k_ \) direction has spin \(\uparrow\). For the opposite electric field, this situation is reversed. From our model, an applied electric field always reduces the (indirect) band gap, irrespective of the sign of the gate voltage. To explain the STM gate dependence, we consider the density of states on the top layer. In Fig. 5a, the bands are colored according to the projection of the electronic states onto the top Te atoms, which we expect to be the most accessible to the STM probe. For a negative gate voltage, the states in the conduction band near \(k_ \pm\) that are pushed downward by the spin splitting are primarily located on the top Te atoms while the states pushed upward are primarily on the bottom Te atoms. For positive gate voltage, the situation is reversed. Since we expect the STM to have a preferential coupling to the top Te atoms this scenario predicts that the STMobserved gap should decrease for negative gate and increase for positive gate, in clear alignment with the experimental results.
In Fig. 5b, c we plot the gap and the calculated \({{{\mathrm{d}}}}I/{{{\mathrm{d}}}}V\) spectra projected on the top Te atoms, as a function of electric field. The spectra are obtained by calculating the projected density of states (PDOS) of the Wannier functions of only the top Te atoms, i.e.,\({{{\mathrm{d}}}}I/{{{\mathrm{d}}}}V_{\it{\epsilon }} \propto \mathop {\sum }\nolimits_i \left \langle{\phi _i{{{\mathrm{}}}}\psi } \rangle\right^2\), where i runs through all the Wannier orbitals of the top Te atoms. The results of the calculations shown in Fig. 5b, c agree well with the behavior of the experimentally measured gap with electric field as shown in Fig. 4f. For the 300 nm SiO_{2} gate oxide, the 80 V gate voltage results in an electric field on the order of 100 mV Å^{−}^{1}. A more accurate determination of the electric field strength is difficult because the thickness of the SiO_{2} can show variations and graphene can induce some degree of screening. Nevertheless, using the value of 100 mV Å^{−}^{1} as an estimate, we find that the change in the bulk gap with gate voltage (as measured from the top surface) to be 0.377(4) meV mV^{−1}, which is in excellent agreement with the experimental value of 0.39(2) meV mV^{−1}.
As an additional check, we confirm this mechanism for the decrease in gap magnitude with gate electric field by considering a minimal fourband tightbinding model constructed from a crystal symmetry analysis and fitted to firstprinciples calculations of the band structure^{21}. Consistent with the DFTderived tightbinding model, we find that the spinsplitting of the conduction band by the electric field is responsible for the observed behavior of the gap. We discuss this minimal model and present calculations of the surface gap electric field dependence in the Supplementary Information.
Our work highlights the sensitivity of the band structure of monolayer 1 T′WTe_{2} to electric fields, which cause large changes in the magnitude of the bulk band gap. Electronic structure calculations show that the effects due to electric fields can be primarily attributed to broken inversion symmetry and strong spinorbit coupling akin to the Rashba effect, rather than electronelectron interaction effects. These systematic studies resolve the puzzlingly large variations in the gap magnitudes that have been previously observed in monolayer 1 T′WTe_{2} (see Supplementary Fig. 3). Indeed, we expect that the gap variations observed in the literature in the monolayer thin films may be attributed to electric fields arising from variations in the local potential induced by the substrate. This is consistent with our STM data on monolayer films grown without RHEED, which show far smaller variations in gap magnitude as shown in Supplementary Fig. 4c. Finally, it is worth highlighting our finding that the gate electric field can generate a spinsplitting of tens of meV in the 2D bulk bands. This substantial spinsplitting provides a new avenue to realizing proximity induced nontrivial superconductivity and Majorana bound states in a tunable system.
Methods
Film growth
GrapheneonSiC substrates were fabricated directly on crystalline SiC in vacuum, providing a highquality graphene surface for subsequent epitaxial growth. WTe_{2} films grown on graphene on SiC were transferred directly to the STM using a vacuum suitcase without exposure to air.
For gating studies, commercial graphene on SiO_{2} substrates was used. These substrates were prepared by transferring monolayer CVD graphene onto a pdoped Si wafer coated with a 300 nm thermal SiO_{2}. Monolayer WTe_{2} was grown using a custom MBE setup. Prior to growth, Gr/SiO_{2}/Si substrates were annealed in ultrahigh vacuum (UHV) for 10 h at 450 °C. The film was grown by coevaporation of elemental W (3 N purity) and Te (6 N purity) while the substrate was held at T = 280 °C. Te was evaporated from a Knudsen cell with a rate of 0.01 Å s^{−1}. W was evaporated using an electron beam evaporator at a rate of 0.18 Å h^{−1}. Monolayer film with 60% coverage was grown in 5 h, thus having the rate of approximately one monolayer per 8.5 h. Such slow growth and 200:1 Te to W flux ratio were necessary to grow highquality monolayer films. After growth, the film was annealed in UHV at 300 °C for 1 h, cooled down to room temperature and capped with 15 nm of Te. The capped film was then transferred to the gating sample holder, which is a threelead holder, one of which serves as the STM bias lead and the other two are connected to the heating W filament (see Supplementary Fig. 1). Once transferred to the STM system, the sample was ionmilled for 10 s using an Ar+ beam at 400 V voltage and 4 µA beam current and then annealed at 200 °C for 1 h to remove the Te cap. The samples were immediately transferred into the STM stage kept at 4 K.
DFT details
The DFT calculations are performed using Quantum ESPRESSO 6.5^{22,23}. In order to compute the detailed band structure, we use Wannier interpolation. We derived a tightbinding model on a 56spinor Wannier basis (W: s and d, Te: s and p) using Wannier90^{24,25}. The tightbinding Hamiltonian is constructed and solved using the opensource code TBmodels^{26}.
Data availability
All data presented in this work are available from the corresponding authors upon request.
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Acknowledgements
STM studies were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), Materials Sciences and Engineering Division under Award No. DESC0022101. Gating and MBE growth and characterization were supported by the Gordon and Betty Moore Foundation’s EPiQS initiative through Grant No. GBMF9465. Y.C. and L. K. W. were supported by a grant from the Simons Foundation as part of the Simons Collaboration on the manyelectron problem. The calculations made use of the computational resources provided by Illinois Campus Cluster and Blue Waters. M.R.H and T.H thank the US DOE for support under award DESC0020128. Y.C. thanks J. Zeng for discussions.
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Y.M. and V.M. designed the experiments. Y.M., G.C., W.S. contributed to thin film growth. Y.M. carried out STM and gating studies and did the data analysis. Y.C., M.R.H., T.H., and L.W. did the theoretical modelling and calculations. All authors contributed to writing the paper.
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Maximenko, Y., Chang, Y., Chen, G. et al. Nanoscale studies of electric field effects on monolayer 1T′WTe_{2}. npj Quantum Mater. 7, 29 (2022). https://doi.org/10.1038/s4153502200433x
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DOI: https://doi.org/10.1038/s4153502200433x
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