The recent discovery of a Weyl semimetal in TaAs offers the first Weyl fermion observed in nature and dramatically broadens the classification of topological phases. However, in TaAs it has proven challenging to study the rich transport phenomena arising from emergent Weyl fermions. The series MoxW1−xTe2 are inversion-breaking, layered, tunable semimetals already under study as a promising platform for new electronics and recently proposed to host Type II, or strongly Lorentz-violating, Weyl fermions. Here we report the discovery of a Weyl semimetal in MoxW1−xTe2 at x=25%. We use pump-probe angle-resolved photoemission spectroscopy (pump-probe ARPES) to directly observe a topological Fermi arc above the Fermi level, demonstrating a Weyl semimetal. The excellent agreement with calculation suggests that MoxW1−xTe2 is a Type II Weyl semimetal. We also find that certain Weyl points are at the Fermi level, making MoxW1−xTe2 a promising platform for transport and optics experiments on Weyl semimetals.
The recent discovery of the first Weyl semimetal in TaAs has opened a new direction of research in condensed matter physics1,2,3,4,5. Weyl semimetals are fascinating because they give rise to Weyl fermions as emergent electronic quasiparticles, have an unusual topological classification closely related to the integer quantum Hall effect, and host topological Fermi arc surface states6,7,8,9,10,11,12,13,14,15. These properties give rise to many unusual transport phenomena, including negative longitudinal magnetoresistance from the chiral anomaly, an anomalous Hall effect, the chiral magnetic effect, non-local transport and novel quantum oscillations16,17,18. Although many recent works have studied transport properties in TaAs (refs 19, 20, 21), transport experiments are challenging because TaAs and its isoelectronic cousins have a three-dimensional crystal structure with irrelevant metallic bands and many Weyl points. As a result, there is a need to discover new Weyl semimetals better suited for transport and optics experiments and eventual device applications.
Recently, the MoxW1−xTe2 series has been proposed as a new Weyl semimetal22,23,24,25. Unlike TaAs, MoxW1−xTe2 has a layered crystal structure and is rather widely available as large, high-quality single crystals. Indeed, MoTe2, WTe2 and other transition metal dichalcogenides are already under intense study as a platform for novel electronics26,27,28,29,30. Moreover, MoxW1−xTe2 offers the possiblity to realize a tunable Weyl semimetal, which may be important for transport measurements and applications. Recently, it was also discovered theoretically that WTe2 hosts a novel type of strongly Lorentz-violating Weyl fermion, or Type II Weyl fermion, long ignored in quantum field theory23,31,32,33,34,35,36,37,38. This offers a fascinating opportunity to realize in a crystal an emergent particle forbidden as a fundamental particle in particle physics. There are, moreover, unique transport signatures associated with strongly Lorentz-violating Weyl fermions23,31,32,33,39,40. For all these reasons, there is considerable interest in demonstrating that MoxW1−xTe2 is a Weyl semimetal. At the same time, it is important to note that ab initio calculations predict that the Weyl points in MoxW1−xTe2 are above the Fermi level22,24,25. This makes it challenging to access the Weyl semimetal state with conventional angle-resolved photoemission spectroscopy (ARPES). Recently, we have demonstrated that we can access the unoccupied band structure of MoxW1−xTe2 by pump-probe ARPES to the energy range necessary to study the Weyl points and Fermi arcs41. As a further consideration, despite the promise of MoxW1−xTe2 for transport, if the Weyl points are far from the Fermi level, then the novel phenomena associated with the emergent Weyl fermions and violation of Lorentz invariance will not be relevant to the material’s transport properties.
Here we report the discovery of a Weyl semimetal in MoxW1−xTe2 at doping x=25%. We use pump-probe ARPES to study the band structure above the Fermi level and we directly observe two kinks in a surface state band. We interpret the kinks as corresponding to the end points of a topological Fermi arc surface state. We apply the bulk-boundary correspondance and argue that since the surface state band structure includes a topological Fermi arc, MoxW1−xTe2 is a Weyl semimetal42. The end points of the Fermi arc also allow us to fix the energy and momentum locations of the Weyl points. We find excellent agreement with our ab initio calculation. However, crucially, we find that certain Weyl points have lower binding energy than expected from calculation and, in fact, are located very close to the Fermi level. This unexpected result suggests that our Mo0.25W0.75Te2 samples may be useful to study the unusual transport phenomena of Weyl semimetals and, in particular, those particularly exotic phenomena arising from strongly Lorentz-violating Weyl fermions. Our work also sets the stage for the first tunable Weyl semimetal. Our discovery of a Weyl semimetal in MoxW1−xTe2 provides the first Weyl semimetal outside the TaAs family, as well as a Weyl semimetal which may be tunable and easily accessible in transport studies. Taken altogether with calculation, our experimental results further show that we have realized the first Weyl semimetal with Type II, or strongly Lorentz-violating, emergent Weyl fermions.
Overview of the crystal and electronic structure
We first provide a brief background of MoxW1−xTe2 and study the band structure below the Fermi level. WTe2 crystallizes in an orthorhombic Bravais lattice, space group Pmn21 (#31), lattice constants a=6.282 Å, b=3.496 Å and c=14.07 Å, as shown in Fig. 1a (ref. 43). Crucially, the crystal has no inversion symmetry, a requirement for a Weyl semimetal12. The crystals we study are flat, shiny, layered and beautiful, see Fig. 1b. The natural cleaving plane is (001), with surface and bulk Brillouin zones, as shown in Fig. 1c. We first consider the overall band structure of WTe2. There are two bands, one electron and one hole pocket, near the Fermi level, both very near the Γ point of the bulk Brillouin zone, along the Γ−Y line. Although the bands approach each other and Weyl points might be expected to arise where the bands cross, it is now understood that WTe2 is in fact very close to a phase transition between a Weyl semimetal phase and a trivial phase, so that the electronic structure of WTe2 is too fragile to make it a compelling candidate for a Weyl semimetal22. Next, we interpolate between ab initio Wannier function-based tight-binding models for WTe2 and MoTe2 to study MoxW1−xTe2 at arbitrary x (ref. 22). For a wide range of x, we find a robust Weyl semimetal phase22. In Fig. 1e,f, we show where the Weyl points sit in the Brillouin zone. They are all located close to Γ in the kz=0 momentum plane. There are two sets of Weyl points, W1 at binding energies EB=−0.045 eV and W2 at EB=−0.066 eV, all above the Fermi level EF. In addition, the Weyl points are almost aligned at the same ky=±kW, although this positioning is not known to be in any way symmetry-protected. We also note that the Weyl cones are all tilted over, corresponding to strongly Lorentz-violating or Type II Weyl fermions, see Fig. 1g (ref. 23). Next, we study a Fermi surface of MoxW1−xTe2 at x=45% using incident light with photon energy hν=6.36 eV, shown in Fig. 1h. We observe two pockets, a palmier-shaped pocket closer to the point of the surface Brillouin zone and an almond-shaped pocket sitting next to the palmier pocket, further from . The palmier pocket is a hole pocket, while the almond pocket is an electron pocket41. We note that we see an excellent agreement between our results and an ab initio calculation of MoxW1−xTe2 for x=40%, shown in Fig. 1i. At the same time, we point out that the electron pocket of the Weyl points is nearly absent in this ARPES spectrum, possibly due to low photoemission cross section at the photon energy used22,41. However, as we will see below, we do observe this electron pocket clearly in our pump-probe ARPES measurements, carried out at a slightly different photon energy, hν=5.92 eV. On the basis of our calculations and preliminary ARPES results, we expect that the Weyl points sit above the Fermi level, where the palmier and almond pockets approach each other. We also present an EB-kx spectrum in Fig. 1j, where we see how the plamier and almond pockets nest into each other. We expect the two pockets to chase each other as they disperse above EF, giving rise to Weyl points, see Fig. 1k.
Unoccupied band structure of MoxW1−xTe2
Next, we show that pump-probe ARPES at probe photon energy hν=5.92 eV gives us access to the bulk and surface bands participating in the Weyl semimetal state in Mo0.25W0.75Te2, both below and above EF. In Fig. 2a–c, we present three successive ARPES spectra of Mo0.25W0.75Te2 at fixed ky near the predicted position of the Weyl points. We observe a beautiful, sharp band near EF, whose sharp character suggests that it is a surface band, and broad continua above and below the Fermi level, whose broad character suggests that they are bulk valence and conduction bands. In Fig. 2d–f, we show the same cuts, with guides to the eye to mark the bulk valence and conduction band continua. We also find that we can track the evolution of the bulk valence and conduction bands clearly in our data with ky. Specifically, we see that both the bulk valence and conduction bands disperse toward negative binding energies as we sweep ky closer to . At the same time, we note that the bulk valence band near is only visible near kx∼0 and drops sharply in photoemission cross-section away from kx∼0. In Fig. 2g,h we present a comparison of our ARPES data with an ab initio calculation of Mo0.25W0.75Te2 (ref. 22). We also mark the location of the three successive spectra on a Fermi surface in Fig. 2i. We include as well the approximate locations of the Weyl points, as expected from calculation. We find excellent correspondence between both bulk and surface states. We add that we directly observe an additional surface state detaching from the bulk conduction band well above the Fermi level and that we can also match this additional surface state well between our ARPES spectra and calculation. Our pump-probe ARPES results clearly show both the bulk and surface band structure of Mo0.25W0.75Te2, both below and above EF, and with an excellent correspondence with calculation.
Observation of a topological Fermi arc above the Fermi level
Now we show that we observe signatures of a Fermi arc in Mo0.25W0.75Te2. We consider the cut shown in Fig. 3a, repeated from Fig. 2b, and we study the surface state. We observe two kinks in each branch, at EB∼−0.005 eV and EB∼−0.05 eV. This kink is a smoking-gun signature of a Weyl point42. We claim that each kink corresponds to a Weyl point and that the surface state passing through them includes a topological Fermi arc. To show these kinks more clearly, in Fig. 3b, we show a second derivative plot of the spectrum in Fig. 3a. In Fig. 3c we also present a cartoon of the kink in our data, with the positions of the W1 and W2 Weyl points marked. Again, note that although the W1 and W2 are not located strictly at the same ky, we expect the ky separation to be on the order of 10−4 Å−1 from calculation, so that we can consider them to lie at the same ky within experimental resolution. We emphasize that from our pump-probe ARPES spectrum, we can directly read off that the energy separation of the Weyl points is ∼0.05 eV and that the W1 are located at ∼−0.005 eV. We also present a quantitative analysis of our data, showing a kink. To do this, we fit the surface state momentum distribution curves (MDCs) to a Lorentzian distribution and we plot the train of peaks corresponding to the surface state band. We note that we simultaneously fit the topological surface state, the bulk valence and conduction states, and the trivial surface state above the conduction band. In Fig. 3d we plot the resulting band dispersions in white and observe an excellent fit to our spectrum. Next, we define a kink as a failure of the train of Lorentzian maxima to fit to a quadratic band. In particular, over a small energy and momentum window, any band should be well-characterized by a quadratic fit, so the failure of such a fit in a narrow energy window implies a kink. After fitting the topological surface state to a quadratic polynomial we find two mismatched regions, marked in Fig. 3e, demonstrating two kinks. For comparison, we plot the energy positions of the W1 and W2 as read off directly from Fig. 3a. We find an excellent agreement between the qualitative and quantitative analysis, although we note that the fit claims that the W2 kink is lower in energy. To illustrate the success of the Lorentzian fit, in Fig. 3f,g we present two representative MDCs at energies indicated by the green arrows. We see that the Lorentzian distributions provide a good fit and take into account all bands observed in our spectra. The raw data, the second derivative plots and the Lorentzian fitting all show two kinks, providing a strong signature of Fermi arcs.
To show that we have observed a topological Fermi arc, we compare our experimental observation of two surface state kinks with a numerical calculation of Mo0.25W0.75Te2. In Fig. 4a,b, we mark the energies of the Weyl points as well as the band minimum of the surface state in our ARPES spectrum and in calculation. We see that the energy difference between the Weyl points is ∼0.02 eV in calculation but ∼0.05 eV in experiment. Moreover, the band minimum Emin is at ∼EF in calculation, but at EB∼0.06 eV in experiment. The difference in Emin suggests either that our sample is electron-doped or that the ky position of the Weyl points differs in experiment and theory. Next, crucially, we observe that, in disagreement with calculation, the W1 are located only ∼0.005 eV above EF. This suggests that the Weyl points and Fermi arcs in our Mo0.25W0.75Te2 samples may be accessible in transport. This result is particularly relevent because MoTe2, WTe2 and other transition metal dichalcogenides are already under study as platforms for novel electronics26,27,28,29,30. Since the Weyl points of MoxW1−xTe2 may be at the Fermi level, it is possible that transport measurements may detect a signature of the strongly Lorentz-violating Weyl fermions or other unusual transport phenomena associated with Weyl semimetals in MoxW1−xTe2. We summarize our results in Fig. 4c. We directly observe, above the Fermi level, a surface state with two kinks (shown in red). By comparing our results with ab initio calculation, we confirm that the kinks correspond to Weyl points. Furthermore, the excellent agreement of our experimental results with calculation shows that we have realized the first Type II Weyl semimetal.
Limits on directly observing Type II Weyl cones
So far we have studied the surface states of MoxW1−xTe2 and we have argued that MoxW1−xTe2 is a Weyl semimetal because we observe a topological Fermi arc surface state. However, topological Fermi arcs cannot strictly distinguish between bulk Weyl cones that are of Type I or Type II. While the excellent agreement with calculation suggests that MoxW1−xTe2 is a Type II Weyl semimetal, we might ask if we can directly observe a Type II Weyl cone in MoxW1−xTe2 by ARPES. This corresponds to observing the two branches of the bulk Weyl cone, as indicated by the purple dotted circles in Fig. 4c. We reiterate that one crucial obstacle in observing a Type II Weyl cone is that all the recent calculations on WTe2, MoxW1−xTe2 and MoTe2 predict that all Weyl points are above the Fermi level22,23,24,25. As we have seen, using pump-probe ARPES, we are able to measure the unoccupied band structure and show a Fermi arc. However, in our pump-probe ARPES measurements, we find that the photoemission cross-section of the bulk bands is too weak near the Weyl points. At the same time, our calculations suggest that for a reasonable quasiparticle lifetime and spectral linewidth, it may be difficult to resolve the two branches of the Weyl cone. We conclude that it is challenging to directly access the Type II Weyl cones in MoxW1−xTe2.
Considerations regarding trivial surface states
One obvious concern in the interpretation of our experimental result is that we observe two kinks in the surface state, but we expect a disjoint segment based on topological theory. In particular, all calculations show that all Weyl points in MoxW1−xTe2 have chiral charge ±1 (refs 22, 23, 24, 25). However, our observation of a kink suggests that there are two Fermi arcs connecting to the same Weyl point, which requires a chiral charge of ±2. To resolve this contradiction, we study the calculation of the surface state near the Weyl points, shown in Fig. 4g. We observe, as expected, a Fermi arc (red arrow) connecting the Weyl points. However, at the same time, we see that trivial surface states (yellow arrows) from above and below the band crossing merge with the bulk bands in the vicinity of the Weyl points. As a result, there is no disjoint arc but rather a large, broadband surface state with a ripple arising from the Weyl points. We can imagine that this broadband surface state exists even in the trivial phase. Then, when the bulk bands cross and give rise to Weyl points, a Fermi arc is pulled out from this broadband surface state. At the same time, the remainder of the broadband surface state survives as a trivial surface state. In this way, the Fermi arc is not disjoint but shows up as a ripple. We observe precisely this ripple in our ARPES spectra of Mo0.25W0.75Te2.
As a further check of our analysis, we perform a Lorentzian fit of an ARPES spectrum at ky shifted away from the Weyl points, shown in Fig. 4d, the same cut as Fig. 2c. We show the Lorentzian fit in Fig. 4e and a quadratic fit to the train of peaks in Fig. 2f. In sharp contrast to the result for ky≈kW, there is no ripple in the spectrum and the quadratic provides an excellent fit. This result is again consistent with our expectation that we should observe a ripple only at ky near the Weyl points. Our results also set the stage for the realization of the first tunable Weyl semimetal in MoxW1−xTe2. As we vary the composition, we expect to tune the relative separation of the Weyl points and their position in energy relative to EF. In Fig. 4h–k, we present a series of calculations of MoxW1−xTe2 for x=10, 25, 40 and 100%. We see that the separation of the Weyl points increases with x and that the W1 approach EF for larger x. We propose that a systematic composition dependence can demonstrate the first tunable Weyl semimetal in MoxW1−xTe2.
We have demonstrated a Weyl semimetal in MoxW1−xTe2 by directly observing kinks and a Fermi arc in the surface state band structure. Taken together with calculation, our experimental data show that we have realized the first Type II Weyl semimetal, with strongly Lorentz-violating Weyl fermions. We point out that in contrast to concurrent works on the Weyl semimetal state in MoTe2 (refs 44, 45, 46, 47, 48, 49, 50, 51, 52), we directly access the unoccupied band structure of MoxW1−xTe2 and directly observe a Weyl semimetal with minimal reliance on calculation. In particular, our observation of a surface state kink at a generic point in the surface Brillouin zone requires that the system be a Weyl semimetal42. The excellent agreement with calculation serves as an additional, independent check of our experimental results. We also reiterate that unlike MoTe2, MoxW1−xTe2 opens the way to the realization of the first tunable Weyl semimetal. Lastly, we note that MoTe2 is complicated because it is near a critical point for a topological phase transition. Indeed, one recent theoretical work24 shows that MoTe2 has four Weyl points, while another25 finds eight Weyl points. This is, moreover, similar to the case of WTe2, which is near the critical point for a transition between eight Weyl points and zero Weyl points. By contrast, MoxW1−xTe2 sits well within the eight Weyl point phase for most x, as confirmed explicity here and by calculation in ref. 22. The stability of the topological phase of MoxW1−xTe2 simplifies the interpretation of our data. By directly demonstrating a Weyl semimetal in MoxW1−xTe2, we provide not only the first Weyl semimetal beyond the TaAs family, but the first Type II Weyl semimetal, as well as a Weyl semimetal which may be tunable and which may be more accessible for transport and optics studies of the fascinating phenomena arising from emergent Weyl fermions in a crystal.
Pump-probe ARPES measurements were carried out using a hemispherical Scienta R4000 analyser and a mode-locked Ti:Sapphire laser system that delivered 1.48 eV pump and 5.92 eV probe pulses at a repetition rate of 250 kHz (ref. 53). The time and energy resolution were 300 fs and 15 meV, respectively. The spot diameters of the pump and probe lasers at the sample were 250 and 85 μm, respectively. Measurements were carried out at pressures <5 × 10−11 Torr and temperatures ∼8 K.
Single crystals of MoxW1−xTe2 were grown using a chemical vapor transport technique with iodine as the transport agent. Stoichiometric Mo, W and Te powders were ground together and loaded into a quartz tube with a small amount of I. The tube was sealed under vacuum and placed in a two-zone furnace. The hot zone was maintained at 1,050 °C for 2 weeks and the cold zone was maintained at 950 °C. The dopant distribution is not uniform particularly near the crystal surface. The composition of the selected sample was determined by an energy dispersive spectroscopy measurement with a scanning electron microscope.
Ab initio calculations
The ab initio calculations were based on the generalized gradient approximation54 using the full-potential projected augmented wave method55,56 as implemented in the VASP package57. Experimental lattice constants were used for both WTe2 (ref. 58) and MoTe2. A 15 × 11 × 7 Monkhorst-Pack k-point mesh was used in the computations. The spin-orbit coupling effects were included in calculations. To calculate the bulk and surface electronic structures, we constructed first-principles tight-binding model Hamilton by projecting onto the Wannier orbitals59,60,61, which use the VASP2WANNIER90 interface62. We used W d orbitals, Mo d orbitals, and Te p orbitals to construct Wannier functions and without perform the procedure for maximizing localization. The electronic structure of the MoxW1−xTe2 samples with finite doping was calculated by a linear interpolation of tight-binding model matrix elements of WTe2 and MoTe2. The surface states were calculated from the surface Green’s function of the semi-infinite system63,64.
The data relevant to the findings of this study are available from the corresponding authors on reasonable request.
How to cite this article: Belopolski, I. et al. Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2. Nat. Commun. 7, 13643 doi: 10.1038/ncomms13643 (2016).
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I.B. thanks Yun Wu, Daixiang Mou, Lunan Huang and Adam Kaminski for collaboration on the conventional laser ARPES measurements and insightful discussions on MoxW1−xTe2 and MoTe2. Work at Princeton University by I.B., D.S.S., S.-Y.X., H.Z., N.A. and G.B. is supported by the US Department of Energy under Basic Energy Sciences Grant No. DOE/BES DE-FG-02-05ER46200 and Princeton University funds (M.Z.H.). Additional support is provided by the Gordon and Betty Moore Foundation under Grant No. GBMF4547. I.B. acknowledges the support of the US National Science Foundation GRFP. Y.I. is supported by the Japan Society for the Promotion of Science, KAKENHI 26800165. T.-R.C. and H.-T.J. were supported by the National Science Council, Taiwan. H.-T.J. also thanks the National Center for High-Performance Computing, Computer and Information Network Center National Taiwan University, and National Center for Theoretical Sciences, Taiwan, for technical support. M.N. is supported by start-up funds from the University of Central Florida. X.C.P., Y.S., H.J.B., G.H.W and F.Q.S. thank the National Key Projects for Basic Research of China (grant nos. 2013CB922100, 2011CB922103), the National Natural Science Foundation of China (grant nos. 91421109, 11522432 and 21571097) and the NSF of Jiangsu province (No. BK20130054). This work is also financially supported by the Singapore National Research Foundation under NRF award no. NRF-NRFF2013-03 (H.L.); NRF Research Fellowship (NRF-NRFF2011-02) and the NRF Medium-sized Centre program (G.E.) and NRF RF award no. NRF-RF2013-08, the start-up funding from Nanyang Technological University (M4081137.070) (Z.L.).
The authors declare no competing financial interests.
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Belopolski, I., Sanchez, D., Ishida, Y. et al. Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2. Nat Commun 7, 13643 (2016). https://doi.org/10.1038/ncomms13643
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