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Strain Tunable Semimetal-Topological-Insulator Transition in Monolayer 1T'-WTe2

A quantum spin hall insulator(QSHI) is manifested by its conducting edge channels that originate from the nontrivial topology of the insulating bulk states. Monolayer 1T'-WTe2 exhibits this quantized edge conductance in transport measurements, but because of its semimetallic nature, the coherence length is restricted to around 100 nm. To overcome this restriction, we propose a strain engineering technique to tune the electronic structure, where either a compressive strain along a axis or a tensile strain along b axis can drive 1T'-WTe2 into an full gap insulating phase. A combined study of molecular beam epitaxy and in-situ scanning tunneling microscopy/spectroscopy then confirmed such a phase transition. Meanwhile, the topological edge states were found to be very robust in the presence of strain.

WTe2, and the gap size is positively related with lattice constant b and negatively related with a (a and b are marked in Fig. 1(a)), consistently with the theoretical results. Moreover, the topological edge states are obtained on both semimetallic and insulating WTe2 islands, indicating that the nontrivial topology is robust in the presence of external strains. Our results unambiguously demonstrate the feasibility of strain engineering to realize the fully gapped QSHI in monolayer 1T'-WTe2, making 1T'-WTe2 a suitable material platform for developing controllable topological electronic devices with a long coherence length.
Monolayer 1T'-WTe2 has a rectangular unit cell as shown in Fig. 1(a), where one W-atom layer is sandwiched between two Te-atom layers. Moreover, there is a Peierls distortion along the a axis, inducing a large band inversion at Г point and driving monolayer 1T'-WTe2 into a Z2 topological phase [1]. However, a finite overlap between the valence band and conduction band renders it semimetallic [1,22]. To determine a suitable approach to manipulate the band structures, we first analyzed the orbital compositions of states at Г point around the Fermi level.
As shown in Fig. 1(b), the states of the conduction and valence bands (marked out by gray dashed boxes) are dominated by orbitals from W atoms and orbitals from Te atoms, respectively (contributions from various orbitals are shown in Fig. S1). The spatial distributions of these orbital wave functions are plotted schematically in Fig. 1 Thus, tensile strain along the b direction can also remove the band overlap. The strain effects along the z direction were also studied and shown in supplementary material II [23].
The responses to the strain from the orbital analysis above is confirmed by the first-principles calculations (more details in supplementary material III [23]). The fundamental gap values (calculated using the HSE03 hybrid functional [24,25]) as a function of strains along the a and b directions are shown in Fig. 1(d) and 1(e), respectively. It is clear that the monolayer 1T'- WTe2 tends to open a fundamental gap under a compressive (tensile) strain along a (b) direction.
Calculations using different exchange-correlation functionals, including generalized-gradient approximation [26] and local-density approximation [27], show similar strain responses, as shown in Fig. S5. All the results indicate that the band structures of monolayer 1T'-WTe2 can be manipulated effectively by strain to realize a full gap insulator.
To confirm the theoretical finding, we fabricated strained monolayer 1T'-WTe2 using MBE and systematically investigated the strain effects using STM/STS. After many attempts, we found the strain can be induced by using a distorted graphene substrate treated by over-heating 6H-SiC (see experimental details in methods [23]). The topography and atomic resolved image in a flat region (see Fig. 2(a)) confirm the quality of the WTe2 films. The measured lattice constants are a = 6.45±0.03 Å and b = 3.46±0.03 Å, respectively. The dI/dV spectra taken from different flat regions are shown in Fig. 2(c), which show uniform semimetallic characters. The minimum of the local density of states (LDOS) is ~ 60 meV below the Fermi level (manifested as a dip) and a V-shape gap locates at zero bias, consistent with previous STM results [5,22]. This V-shape gap is the Coulomb gap resulting from the electron-electron interactions in monolayer WTe2, which always exists while the LDOS at the Fermi level is nonzero [5,22].
When the substrate is deformed, the crystal structure of WTe2 films grown on it will also be distorted. Figure 2 Different from the flat regions, the dI/dV spectra of distorted regions are non-uniform and may exhibit either semimetallic behavior with a dip and a V-shape coulomb gap ( Fig. 2(d)) or insulating behavior with a large U-shape gap ( Fig. 2(e) and 2(f)). In addition, the size of the Ushape insulating gap in different areas also differs (also see Fig. S6 (a)). From the spatially resolved spectra in Fig. S3, S6 (a) and S7, one can see that the U-shape gap exhibits clear straindependence, especially in Fig. S3, where the U-shape gap starts from a dip below the Fermi level and gradually becomes a full gap with zero LDOS when the strain is large enough. During this process, the V-shape coulomb gap is initially unchanged and eventually disappears when the LDOS around Fermi level becomes zero because of the increased U-shape gap. In addition, we also doped the WTe2 films with potassium (K) atoms to shift the Fermi level to exclude the effect of Coulomb interactions on the gap. As shown in the Fig. 2(g), the Fermi level is upper shifted ~40 meV and the dip now resides around -100 meV. At some locations in distorted regions, the strain induced U-shape gap still holds even though the Fermi level is far from it.
Thus, we can safely rule out the possibility that the insulating gaps are caused by coulomb blockage or other types of many-body effect. The influences of substrates are also excluded in supplementary material V [23]. Combining all the evidence above, it is reasonable to deduce that the insulating gap is induced by strain, and we further performed a more detailed study of gap size and lattice constants.
We took dozens of sets of experimental data in different areas of distorted regions, and each set includes a gap value and the corresponding in-plane lattice constants (a, b). As shown in Fig. 3(a), the gap decreases with a but increases with b, and is zero when a is large and b is small. To study uniaxial dependency of gap on lattice constants a and b quantitatively, we regrouped the data and averaged the gaps with the similar a or b in Fig. 3(b) and (c). We examined the analysis very carefully to rule out any artefact caused by different choices of averaging methods (see more details in supplementary material VII [23]). We found that the gap will decrease with a over the range from 6.23 Å to 6.54 Å, but increase with b over the range from 3.49 Å to 3.57 Å. In addition, the gap closes when a is larger than 6.54 Å (~ 1.40% tensile strain) or b is smaller than 3.49 Å (~ 0.87% compressive strain). These experimental results are consistent with our theoretical predictions. Besides, the strain effects along the d axis were also qualitatively analyzed in these experiments, as shown in supplementary material II [23].
All the theoretical and experimental results above clearly demonstrate that in-plane strain can indeed be used as an effective tool to tune the band structures of monolayer 1T'-WTe2 and drive a phase transition from a semimetal to an insulator. Now the critical question is whether the nontrivial Z2 topology still holds under strain. To answer this question, we first analyzed the phase diagram for strains between -10% and +10%, as shown in Fig. 4(a). The whole phase diagram is divided into three different regions: insulating nontrivial phase, semimetallic nontrivial phase and semimetallic trivial phase. The first two phases dominate the phase diagram, indicating the persistence of nontrivial topology subject to external strain fields, which is due to the large band inversion at Г point induced by Peierls distortion. All experimental data points are located within these two nontrivial regimes and are represented by black circles in the phase diagram. Moreover, the freestanding WTe2 without strain is near the phase boundary of the insulating nontrivial phase and semimetallic nontrivial phase, which makes the strain a feasible and efficient approach to phase engineering.
In experiments, the gapless states located at edges are strong evidences for QSHI. In flat regions, we obtain edge states similar to previous studies [5] (see Fig. S10), confirming the nontrivial Z2 topology. In distorted regions, we focus on insulating WTe2 islands with a full bulk gap, such as the one shown in Fig. 4(b) (see more examples in Fig. S11). Typical dI/dV spectra taken on it are shown in Fig. 4(c), where a full gap as large as ~ 50 mV is observed in the bulk while metallic spectra are obtained at two edges along both the a and b directions, labeled as A and B edges. It is worth noting that the V-shape coulomb gap at zero bias again appears in the edge states since there are finite LDOS at the Fermi level from the topological edge states, even when there is a large insulating U-shape gap in the bulk states. Using the experimental lattice constants of this WTe2 island, we calculate the band structure along the a direction (in Fig. 4(d)). There are indeed topological edge states spanning the whole bulk gap, which is consistent with the metallic dI/dV spectrum taken at the A edge. Similar results for the B edge are shown in Fig. S12.
Besides confirming the nontrivial topology, we further studied the penetration length of the topological edge states, which is particularly important when designing devices. Two series of dI/dV spectra were measured along the dotted lines in Fig that the quantized conductance can be confined to a narrow channel, which is vital for realizing high-density dissipationless topological devices.
In summary, strain engineering of the band structure of 1T'-WTe2 was theoretically predicted and experimentally confirmed. We found that strain can tune the electronic properties and induce a phase transition from a semimetal to an insulator, while maintaining the nontrivial Z2 topology. The tunable band structure and robust topology make WTe2 a suitable material platform for both fundamental research and topological electronic devices.

Supplementary materials
I. Orbital projections around Fermi level.

II.
Strain effects along z direction.

III.
Confirmation of in-plane strain effects by first-principles calculations.

IV.
Gap as a function of in-plane strains calculated by different exchange-correlation functional.
V. dI/dV spectra in distorted regions.

VI.
Tuning Fermi level by electron doping.
VII. Statistical process to extract the uniaxial relation between gap and lattice a and b.

IX.
Edge states on other insulting WTe2 islands in distorted regions.

X.
Calculated edge states along B-edge.

XI.
Methods.   Since there is only one W atom layer, the related orbital (see Fig. 1(b)) has no explicit bonds along z direction, thus the orbital formed -like bonds dominate the strain reactions, as shown in Fig. S2(a). When increasing/decreasing the atomic layer distance Δd, the -like bonds get weaker/stronger, which will cause an energy increase/decrease of valence band upon a tensile/compressive strain. Thus a compressive strain along z direction can also reduce the band overlap and even open a gap.
Here we tune atomic layer interval d (marked in Fig. 1(a)) to simulate the influences of strains along z direction. As shown in Fig. S2(b) and S2(c), when enlarging Δd with a positive value, the CB (VB) will drop (rise) in energy and as a result the overlap between CB and VB is enhanced. On the contrary, decreasing Δd to a negative value, the CB will increase in energy and the VB will decrease in energy, which reduces the band overlap. Finally, the relation between Δd and gap value is shown in Fig. S2(d), which indicates an insulating gap will open under a proper compressive strain along z direction.  Fig. S3(b), where the LDOS of in-gap states at -9 meV decreases to zero near the bump. Besides, an interference of electronic states is observed, especially for the states lower than -100 mV, which is also observed in 1T'-WSe2 [1]. The data for another bump also show suppression to in-gap states (see Fig. S3(c) and S3(d)), indicating that the bump can uniformly reduce the band overlap. Based on the crystal structure, this gap opening is presumably due to the compress of interlayer distance (negative Δd) by bumps, as mentioned in orbital analysis part.

V.
dI/dV spectra in distorted regions

dI/dV spectra in distorted regions in large scale
Fig. S6. Spatial dependency of dI/dV spectra in distorted regions. (a) Spatial-dependent spectra taken at different locations in a distorted region (100 nm × 100 nm, same region with Fig. 2(b)).
(b) Comparison of electronic states of graphene substrate near insulating and semimetallic WTe2 films.
The spectra taken at flat regions are uniform semimetallic type, unless the edge states emerge, as shown in Fig. 2(c) (also in Fig. S10 below), where the V-shape coulombs gap and a dip below Fermi level always exist unless reaching to film edges, no matter the size of the WTe2 island. Both the dip and the coulomb gap do not reach to zero LDOS. While the spectra taken at different areas of distorted region are distinct, as shown in Fig. 2(d)-(f) and Fig. S6 (a), where the spectra show a remarkable spatial-dependency. An unique insulating type of spectra can be observed at some areas in distorted regions. And the gap size also varies in spatial. These results indicate that the insulating gap is probably related to spatially-dependent distortions.
To exclude the effects of different contributions form graphene substrate in distorted regions and flat regions, we compare the dI/dV spectra of graphene near an insulating WTe2 island with that near a semimetallic WTe2 island, as shown in Fig. S6  The dI/dV spectra results of small areas give a clearer view of the strain-dependent insulating gap, such as shown in Fig. S7(a), where the lattices show clear differences in right and left parts. The semimetallic type of spectra can be observed at the left part, while the insulting spectra exist at the right part. From Fig. S7(c), we can see that the dip at about -60 meV gradually evolves into large insulating gaps, while the coulomb gap residing at Fermi level is nearly unchanged, as long as the LDOS at around Fermi level is non-zero. Figure S7 (d) shows this spatially-dependent variation perfectly. The mapping using the bias inside the insulating gap (-25 meV) gives a phase boundary between semimetal and insulator (see Fig. S7 (b)). To distinguish the strain induced U-shape band gap and coulomb gap and rule out the influences of coulomb interactions, we deposited some potassium (K) on the sample surface in order to dope electrons into WTe2. Before depositing K atoms, the sample was firstly cooled down to 4.2 Kelvin to ensure that the K atoms deposited on WTe2 but not flew away. The measurements were applied on WTe2 sample after 2 min's deposition of K atoms. Figure S8 (a) and S8 (b) shows the WTe2 film in flat regions before/after K-doping, respectively. And the tunneling spectra taken on it show a dip feature below Fermi level as well as a coulomb gap residing at zero bias. Compared with the original spectra, the spectrum after electron-doping has an overall downward shift ~40 meV, and the dip now locates at around -of Fig. S8 (b)). Our results of electron-doping are similar with the previous research [3]. In distorted regions, fully band gaps can be acquired in samples both with (Fig. S8 (c)) and without ( Fig. S8 (d)) electron-doping. It is worth noting that the band gap after electron-doping is far away from the Fermi level and is well separated with the coulomb gap which is still located at zero bias. These indicate that the band gaps opened by strain are irrelevant to Fermi level and are not caused by coulomb interaction. , where n is the number of data points in each interval, ∆ is the averaged gap value within each interval and the summation is made for all data points within each interval. The edge states on semimetallic islands are similar to previous STM studies [4]. Figure S10(a) shows a small island of WTe2 in flat region. In the bulk of the island, a semimetallic dI/dV spectrum with the intensity minimum of LDOS at ~ -60mV is acquired (green curve in Fig.   S10(b)). Spectra taken at A-edge and B-edge are also shown in Fig. S10(b), both of which show remarkable increases of intensity around the Fermi level, indicating the existence of edge states.

VIII. Topological edges states on semimetallic WTe2 islands
All three spectra show coulomb gaps at zero bias. The calculated topological edge states along A edge are shown in figure S10(c), confirming the edge states induced enhancement of intensity around Fermi level. The calculated edge states along B edge are shown in Fig. S12(b).
To further investigate the penetration of edge states, two series of dI/dV spectra crossing A and B edges are taken along dotted lines in Fig. S10(a), and their color images are shown in figure S10(d) and S10(e), respectively. It should be noted that the last two points of both lines are locate on the graphene substrate, where the spectra are totally different from that on WTe2.
The dip feature at ~ -64 mV is uniform in the bulk. When approaching to edges, the dip vanishes  Calculated edges states along B edge are shown in Fig. S12. Using the lattice constants of the insulating island shown in Fig. 4(b), the calculated bands along B edge also show the topologically protected edge states, as shown in Fig. S12(a). Similar calculations are applied for the semimetallic island shown in Fig. S10(a), and the results are shown in Fig. S12(b).

Treatments for the substrate
Bilayer graphene created from 6H-SiC (0001) is selected as the substrate to grow monolayer 1T'-WTe2. The 6H-SiC is first heated to 600 ℃ to degas for 12 hours in the MBE chamber with a base pressure of 2×10 -10 Torr. It is then heated to 900 ℃ for 30 mins and then to 1300 ℃ for 10 mins. Finally, it is gradually cooled to room temperature. By this process we obtain a bilayer graphene surface on the 6H-SiC substrate. If the maximum temperature during the heat treatment exceeds 1300 ℃, there are likely to be some surface deformations, such as irregular bends and deep holes.

MBE growth of 1T'-WTe2
The monolayer 1T'-WTe2 films are grown on bilayer graphene by the MBE method in a vacuum chamber with base pressure of 2×10 -10 Torr. The tellurium (Te) source is a knudson diffusion cell and the tungsten (W) source is an electron beam evaporator. The Te source material has a purity of 99.999% and the W has a purity of 99.995%. The flux ratio between W and Te is about 1 : 20. The growth process is monitored by reflection high-energy electron diffraction (RHEED). After growth the sample is annealed at 260 ℃ in a Te environment for 2 hours and then without the Te environment for 30 mins to enhance the film quality.

STM measurement
In situ STM measurements are carried out after sample growth. The STM chamber has a base pressure of 1×10 -10 Torr. The sample is cooled to 4.2 K before all measurements. The topographic images are obtained using a constant current mode. Before gathering data, the STM tip is first calibrated on a silver surface.

First-principles calculations
The calculations are performed in the framework of density functional theory as implemented in the VASP [5] package using the projector augmented wave (PAW) method [6]. The Brillouin zone is sampled in 7 × 14 × 1 Monkhorst-Pack k-point grid, and the energy cutoff of the plane wave basis is 400 eV. We compared the calculations from different exchange-correlation functionals including GGA (Perdew-Wang 91 (PW91), Perdew-Burke-Ernzerhof (PBE)) and LDA, and the results are almost identical. We also used the HSE03 hybrid functional to improve the band gap calculations [7]. Ab-initio based tight-binding calculations were performed using the WANNIER90 interface [8]. The edge states were calculated by the iterative Green's function approach [9].