Large quantum-spin-Hall gap in single-layer 1T′ WSe2

Two-dimensional (2D) topological insulators (TIs) are promising platforms for low-dissipation spintronic devices based on the quantum-spin-Hall (QSH) effect, but experimental realization of such systems with a large band gap suitable for room-temperature applications has proven difficult. Here, we report the successful growth on bilayer graphene of a quasi-freestanding WSe2 single layer with the 1T′ structure that does not exist in the bulk form of WSe2. Using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy/spectroscopy (STM/STS), we observe a gap of 129 meV in the 1T′ layer and an in-gap edge state located near the layer boundary. The system′s 2D TI characters are confirmed by first-principles calculations. The observed gap diminishes with doping by Rb adsorption, ultimately leading to an insulator–semimetal transition. The discovery of this large-gap 2D TI with a tunable band gap opens up opportunities for developing advanced nanoscale systems and quantum devices.

Transition metal dichalcogenides are promising for developing 2D TIs.These layered materials can be easily fabricated in single-layer forms.Some of them containing heavy elements with a strong spin-orbit coupling are predicted to be 2D TIs; notable examples include single-layer 1T′ MX2 (M = Mo or W; X = S, Se, or Te) 16 .Experimental work to date has mostly focused on single-layer WTe2 because the 1T' phase is the stable form in the bulk [17][18][19] , but not necessarily so for the other cases, and W has a very strong atomic spin-orbit coupling.While some of the other MX2 materials can be converted to the 1T' phase by intercalation or strain, the added complexity makes it is difficult to prove the QSH state 20 .WSe2, the material chosen for the present study, exhibits a hexagonal 2H structure in the bulk, which is of great interest for its large indirect band gap and strong spin-valley coupling 21,22 , but the single layer with the 1H structure is not topological.
We show that single layers of WSe2 can be prepared instead in the 1T' phase, which is topological with a gap of 129 meV based on ARPES experiments and 116 meV based on G0W0 calculations.This gap is more than twice as large as that reported for 1T' WTe2 17 , and furthermore, it can be tuned with surface doping to undergo an insulator-semimetal transition.Single-layer 1T' WSe2 is thus an excellent candidate for developing spintronics based on the QSH effect.
Figure 1a shows top and side views of the structure of 1T' and 1H single-layer WSe2.The observed bulk crystal structure is the 2H phase consisting of a van der Waals stack of 1H layers in an ABA sequence.The bulk 1T' structure, if existent (as in WTe2), would involve an ABC stacking of the 1T' layers together with a lattice distortion along the x direction.The surface unit cells and some special points are indicated in Fig. 1b.In our experiment, films of WSe2 were grown in situ on a bilayer-graphene-terminated 6H-SiC(0001) 23 via van der Waals epitaxy 24,25 .Reflection high energy electron diffraction (RHEED) shows that a single-layer WSe2 grown at a substrate temperature of 280 C (Fig. 1c) exhibits a mixture of 1H and 1T' phases, both with sharp diffraction patterns.At higher substrate growth temperatures, the 1H phase becomes more prevalent, and it is the only phase observed at growth temperatures above 400 C (Fig. 1c).The 1T' phase is favored at lower growth temperatures, and it becomes the only phase observed at a growth temperature of 130 C; however, the film quality is poor as evidenced by a fuzzy RHEED pattern (not shown here).Scans of the core levels (Fig. 1d) show splittings of the Se 3d and W 4f states in the mixed phase due to the inequivalent structures; an analysis of the W core level line shape indicates that the 1H and 1T' phases have a coverage ratio of 1.8 on the surface.ARPES maps taken from the single-layer samples at 10 K along the ΓK ̅̅̅̅ direction are shown in Fig. 1e.The pure 1H phase shows a sizable gap below the Fermi level; it is therefore a semiconductor similar to the bulk case 21 .The top valence band at Γ ̅ splits into two branches toward K ̅ because of the strong spin-orbit coupling of W. The valence band maximum is at K ̅ , consistent with prior studies of this phase 24,26 .For the mixed sample, the 1T' phase gives rise to additional valence bands of very different dispersion relations, and the topmost valence band reaches near the Fermi level to form a fairly flat portion around the zone center.For comparison, calculated band structure of the 1T' phase based on the GGA/PBE method is presented in Fig. 2b.This phase is also a semiconductor but with an indirect band gap along the ΓY ̅̅̅̅ direction.A band inversion occurs at Γ ̅ between the W 5d and Se 4p orbitals with opposite parities; spin-orbit coupling causes anti-crossing, giving rise to a gap of Eg = 33 meV based on the calculation (Fig. 2c).The GGA/PBE scheme tends to underestimate semiconductor gaps; a G0W0 calculation yields a more accurate gap value of 116 meV.With an inverted band topology across a spin-orbit gap, the 1T' phase is expected to be a 2D TI.Indeed, our computed topological index Z2 equals 1, confirming that the system is a QSH phase (but not for the 1H phase which is an ordinary insulator).
The 1T' phase has a rectangular lattice (Fig. 1a) instead of a triangular lattice; as a result, it exhibits three domains related by 120 rotations.ARPES spectra taken along ΓY ̅̅̅̅ and ΓX ̅̅̅̅ include contributions from ΓP ̅̅̅̅ and ΓN ̅̅̅̅ , respectively (Fig. 2a).Detailed ARPES maps near the Fermi level for the 1T' phase together with overlaid theoretical band structure along the different directions (Fig. 2d) confirm the mixed-domain configuration.Specifically, the top valence band shows an apparent "splitting" near 0.2 Å -1 , which is a consequence of the domain mixing.The conduction band minimum is clearly seen in Fig. 2d.As indicated, the indirect gap between the valence band maximum and the conduction band minimum is 129 meV, which is very close to the G0W0 value of 116 meV.Notably, it is twice as large as that of the related 2D TI WTe2 17 .The thermal energy kBT is 25 meV at room temperature, and semiconductors must have a gap greater than about 4kBT = 100 meV in order to be useful.Based on this criterion, 1T' WSe2 would be an excellent candidate for QSH applications at ambient temperature.
For better viewing of the conduction bands, we have employed Rb doping to shift the bands downward relative to the Fermi level (Fig. 3a).Interestingly, the changes at higher doping levels cannot be described by a rigid shift of the bands.Specifically, the gap becomes smaller and the conduction and valence band edges eventually cross each other (Fig. 3b) at a doping level of NC = 6 x 10 13 /cm 2 , beyond which the system becomes a semimetal with a negative gap (Fig. 3c).
Moreover, the band shapes become noticeably different.An implication is that Rb deposition leads to, in addition to surface electron doping, structural modifications through incorporation or intercalation of Rb in the lattice 22,27 .The Rb 3d core level line shapes (Fig. 3d) reveal multiple components indicating different Rb sites that vary in population with increasing Rb coverages.
The tunability of the QSH gap can be a useful feature relevant to applications.The insulator-semimetal transition at NC offers a mechanism to switch off the QSH channels.STM/STS measurements in a different chamber performed on a sample with a coverage of 1/2 layer made in the ARPES system transferred under a capping layer through air (see Methods Section) reveal single-layer islands of 1H and 1T' structures and some two-layer islands (Fig. 4a).
STS scans reveal a large band gap for the interior of 1H islands (Fig. 4b) and a much smaller gap for the interior of 1T' islands in agreement with the ARPES data, although the STS data are expected to be thermally broadened at the measurement temperature of 77 K relative to the ARPES data taken at 10 K. Figures 4c and 4d show atom-resolved images of the 1T' and 1H phases, respectively.The orientation of the triangular 1H phase is the same as the underlying bilayer graphene, and the image exhibits a Moiré pattern 24 .The 1T' phase has a rectangular lattice instead (Fig. 1a); all three domain orientations separated by 120 are observed.
Experimental observation of edge states within the gap is a necessary test for QSH systems.
Figure 4e is an STM image with a 1T' island covering the right half only. Figure 4f shows STS curves taken at a point (A) in the island very close to the island edge (green curve A) and another point (B) in the island still near but farther away from the edge (blue curve B); the two points A and B are indicted by the correspondingly color-coded dots in Fig. 4e.With the Fermi level aligned relative to the included ARPES map 28 , the gap is indicated by the two vertical red dashed lines.Also shown is a reference red curve C taken from a point deep inside the island.It shows a clear gap; the small residual tunneling density of states (DOS) within the gap can be attributed to tunneling/coupling to the underlying bilayer graphene.Similar nonzero DOS in the gap is evident in single-layer WTe2 results 17 .Curve A, relative to curve C, shows much higher DOS within the gap, suggesting contributions from edge states 13,14,17 , a key feature of QSH systems; this extra DOS is much reduced for curve B. Details regarding the edge-state contributions are shown in Fig. 4g, where the differential conductance is plotted as a function of x (defined in Fig. 4e) and energy, with the gap indicated by two horizontal dashed lines.A red dashed rectangle in Fig. 4g highlights the enhanced edge conductance within the gap near the island edge.Note that STS can be affected by quasiparticle interference (QPI) effects, as indicated in Fig. 4g; similar effects have been seen in WTe2 29 .For curve A in Fig. 4f, the strong peak at about -170 meV, which might seem strange, is caused by QPI constructive interference (the strongest red spot indicated in Fig. 4g).Despite this complication, the edge-state contribution within the gap is evident.The results are consistent with the earlier conclusion of a QSH system.
To design or search for materials with large QSH gaps, one might be tempted to employ chemical substitution of the constituent atoms of a QSH system with heavier elements in the same column of the periodic table.Our observation of a QSH gap in single-layer 1T' WSe2 about twice as large as that in WTe2 seems counter-intuitive.As discussed above, the QSH gap in WSe2 originates from band inversion of the W 5d and Se 4p states near the zone center and anti-crossing of the bands caused of spin-orbit coupling (Fig. 2c).A similar theoretical analysis for WTe2 shows that the relevant reverse-ordered states near the zone center are both dominated by the W 5d states 30 .
The Te states play a relatively minor role.The self-hybridization of the W 5d states is actually weaker, leading to a smaller QSH gap.
Most single-layer MX2 materials, including WSe2, are stable only in the 1H phase, which gives rise to ordinary semiconductors.Our demonstration of the successful creation of single-layer 1T' WSe2 with a sizable QSH gap offers an important example of materials engineering.Its QSH gap of 129 meV is more than five times the thermal energy kBT at room temperature, suggesting that it is suitable for QSH electronics at ambient temperature.While the system is only metastable, its demonstrated stability up to ~280 C is more than sufficient.For comparison, 1T' WTe2, which has garnered much attention, actually has a smaller QSH gap not conducive to ambienttemperature spintronics.Unlike exfoliated materials, the 1T' WSe2 films grown by molecular beam epitaxy, as demonstrated herein, should be readily adaptable to large-scale fabrication of devices such as topological field effect transistors 16 .Other materials such as superconductors can be added by molecular beam epitaxy, thus offering opportunities to realize additional functionality and novel properties including Majorana fermions.Our work expands the family of large-gap QSH materials and inspires further experimental exploration of novel QSH systems.

Methods
Experimental details.Thin films of WSe2 were grown in situ in the integrated MBE/ARPES systems at beamlines 12.0.1 and 10.0.1, Advanced Light Sources, Lawrence Berkeley National Laboratory.Substrates of 6H-SiC(0001) were flash-annealed for multiple cycles to form a wellordered bilayer graphene on the surface 23 .Films of WSe2 were grown on top the substrate at a rate of 50 minutes per layer by co-evaporating W and Se from an electron-beam evaporator and a Knudsen effusion cell, respectively.The growth of different phases of WSe2 is controlled by the substrate temperature.The 1T' phase starts to form at 130 C but the film quality is poor at low growth temperatures.The best 1T' phase is obtained at near 280 C, but the 1H phase also forms and completely dominates at temperatures at about 400 C.ARPES measurements were performed with an energy resolution of <20 meV and an angular resolution of 0.2.Each sample's crystallographic orientation was precisely determined from the symmetry of constant-energycontour ARPES maps.The surface electron density with Rb doping is determined from the Luttinger area of the Fermi surface around Γ ̅ based on  = g    2 2 22 .For STM/STS measurements, the samples after characterization by ARPES were capped with a 20-nm layer of Se for protection and then shipped and loaded several days later into the STM/STS system, wherein the protective Se layer was thermally desorbed at 250 C before measurements using an Omicron LTSTM instrument and freshly flashed tungsten tips.Experimentation with capping and decapping using the ARPES system reveals that such sample treatments lead to a clean but rougher surface, as evidenced by decreased clarity of the ARPES maps but no detectable impurity core level peaks.
Computational details.First-principles calculations were performed using the Vienna ab initio package (VASP) [31][32][33] with the projector augmented wave method 34,35 .A plane wave energy cutoff of 400 eV and an 8x8x1 k-mesh were employed.The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional 36 was used for structural optimization of single-layer WSe2.Freestanding films were modeled with a 15-Å vacuum gap between adjacent layers in the supercell.The fully optimized in-plane lattice constants for single layer 1T' WSe2 are a = 5.94 Å and b = 3.30 Å.Our results generally agree with those reported in Ref. 15 where available.