Discovery of a new type of topological Weyl fermion semimetal state in MoxW1-xTe2

Abstract

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 Mo_xW_1-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 Mo_xW_1-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 Mo_xW_1-xTe₂ is a Type II Weyl semimetal. We also find that certain Weyl points are at the Fermi level, making Mo_xW_1-xTe₂ a promising platform for transport and optics experiments on Weyl semimetals.

Figure 1. Overview of Mo_xW_1−xTe₂.

(a) The crystal structure of the system is layered, with each monolayer consisting of two Te layers (green) and one W/Mo layer (red). (b) A wonderful scanning electron microscope image of a typical single crystal of Mo_xW_1−xTe₂, x=45%. The layered structure is visible in the small corrugations and breaks in the layers. (c) Bulk and (001) surface Brillouin zone, with high-symmetry points marked. (d) Bulk band structure of WTe₂ along high-symmetry lines. There are two relevant bands near the Fermi level, an electron band and a hole band, both near the Γ point and along the Γ−Y line, which approach each other near the Fermi level. (e,f) On doping by Mo, Mo_xW_1−xTe₂ enters a robust Weyl semimetal phase. Schematic of the positions of the Weyl points in the bulk Brillouin zone. The opposite chiralities are indicated by black and white circles. Crucially, all Weyl points are above the Fermi level. (g) The Weyl cones in Mo_xW_1−xTe₂ are unusual in that they are all tilted over, associated with strongly Lorentz-violating or Type II Weyl fermions, prohibited in particle physics. (h) Fermi surface of Mo_xW_1−xTe₂ at x=45% measured by ARPES at hν=6.36 eV, showing a hole-like palmier pocket and an electron-like almond pocket. (i) There is an excellent correspondence between our ARPES data and our calculation. Note that the k_y axis on the Fermi surface from ARPES is set by comparison with calculation. (j) An E_B–k_x cut showing the palmier and almond pockets below the Fermi level. (k) In summary, the Fermi surface of Mo_xW_1−xTe₂ consists of a palmier hole pocket and an almond electron pocket near the point. The two pockets chase each other as they disperse, eventually intersecting above E_F to give Weyl points.

Figure 2. Dispersion of the unoccupied bulk and surface states of Mo_0.25W_0.75Te₂.

(a–c) Three successive ARPES spectra for Mo_0.25W_0.75Te₂ at fixed k_y near the expected position of the Weyl points, k_W, using pump-probe ARPES at probe hν=5.92 eV. A strong pump response allows us to probe the unoccupied states ∼0.3 eV above E_F, which is well above the expected E_W1 and E_W2. (d–f) Same as (a–c), but with the bulk valence and conduction band continua marked with guides to the eye. We see that we observe all bulk and surface states participating in the Weyl semimetal state. As expected, both the bulk valence and conduction bands move towards more negative binding energies as k_y moves towards . (g,h) Comparison of our calculations with experimental results for k_y∼k_W. As can be seen from panel (h), our spectra clearly display all bulk and surface bands of Mo_0.25W_0.75Te₂ relevant for the Weyl semimetal state, both below and above E_F, and with excellent agreement with the corresponding calculation in panel g. (i) The locations of the cuts in (a–c).

Figure 3. Direct experimental observation of Fermi arcs in Mo_0.25W_0.75Te₂.

(a) To establish Fermi arcs in Mo_0.25W_0.75Te₂ we focus on the spectrum shown in Fig. 2b, with k_y∼k_W. We observe two kinks in the surface state, at E_B∼−0.005 eV and E_B∼−0.05 eV. (b) The kinks are easier to see in a second-derivative plot of panel a. (c) Same as panel a, but with a guide to the eye showing the kinks. The Weyl point projections are at the locations of the kinks. The surface state with the kinks is a topological Fermi arc. (d) To further confirm a kink, we fit Lorentzian distributions to our data. We capture all four bands in the vicinity of the kinks: the bulk conduction and valence states, the topological surface state and an additional trivial surface state merging into the conduction band at more negative E_B. We define a kink as a failure of a quadratic fit to a band. We argue that for a small energy and momentum window, any band should be well-characterized by a quadratic fit and that the failure of such a fit shows a kink. (e) By matching the train of Lorentzian peaks of the topological surface state (red) to a quadratic fit (blue) we find two mismatched regions (shaded in yellow), showing two kinks. The purple arrows show the location of the Weyl points, taken from panel c, and are consistent with the kinks we observe by fitting. (f,g) Two characteristic MDCs at energies indicated by the green arrows in panel e. We see that the Lorentzian distributions provide a good fit and capture all bands observed in our spectra.

Figure 4. Demonstration of a Weyl semimetal in Mo_xW_1−xTe₂.

(a) The same spectrum as Fig. 3a but with the energies E_W1, E_W2, E_min marked. (b) The same energies marked in an ab initio calculation of Mo_0.25W_0.75Te₂. We note that this cut is not taken at fixed k_y–k_W. Instead, we cut along the exact line defined by W₁ and W₂ in the surface Brillouin zone. Since is exceedingly close to , this cut essentially corresponds to our experimental data. The Weyl points are ∼0.05 eV separated in energy in our data, compared with ∼0.02 eV in calculation. In addition, crucially, the W₁ are lower in energy than we expect from calculation and in fact are located only ∼0.005 eV above E_F. (c) A cartoon of our interpretation of our experimental results. We observe the surface state (red) with a kink at the locations of the Weyl points (black and white circles). Each surface state consists of a Fermi arc (middle red segment) and two trivial surface states which merge with bulk bands near the location of the Weyl points. We observe certain portions of the bulk bands (grey), but not the bulk Weyl cones. (d) The same spectrum as Fig. 2c, at k_y shifted toward . (e,f) A Lorentzian fit of the surface state and a quadratic fit to the train of peaks, showing no evidence of a kink. This is precisely what we expect from a cut away from the Weyl points. (g) A close-up of the band inversion, showing a Fermi arc (red arrow) which connects the Weyl points and trivial surface states (yellow arrows) from above and below which merge with the bulk bands in the vicinity of the Weyl points. (h–k) Composition dependence of Mo_xW_1−xTe₂ from first principles, showing that the separation of the Weyl points increases with x. Our observation of a Weyl semimetal in Mo_0.25W_0.75Te₂ sets the stage for the first tunable Weyl semimetal in Mo_xW_1−xTe₂.