Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal ${\mathrm{WTe}}_2$

A kind of topological material, the type-II Weyl semimetal, was proposed recently where the Weyl points emerge at the contact points of the electron and hole pockets, resulting in a highly tilted Weyl cone. In type-II Weyl semimetals, the Lorentz invariance is violated and a different type of Weyl fermion is generated that leads to intriguing physical properties. ${\mathrm{WTe}}_2$ is interesting because it is predicted to be a good candidate for realizing type-II Weyl semimetals. By utilizing laser-based angle-resolved photoemission spectroscopy with high energy and momentum resolutions, we have revealed a full picture of the electronic structure of ${\mathrm{WTe}}_2$. A clear surface state has been identified and its connection with the bulk electronic states in the momentum and energy space shows good agreement with band structure calculations. Our results provide electronic signatures that are consistent with type-II Weyl states in ${\mathrm{WTe}}_2$. They lay a foundation for further investigations on the topological nature of ${\mathrm{WTe}}_2$ and the exploration of unique phenomena and physical properties in type-II Weyl semimetals.

Figure 1

Fermi surface of ${\mathrm{WTe}}_2$ and its comparison with calculated results. (a) Crystal structure of ${\mathrm{WTe}}_2$ in Td form with a space group $Pmn{2}_1$, viewed along the $c$ axis (perpendicular to the stacked layers). The W-W zigzag chains are shown by the red solid line and the direction of the lattice distortion is marked with the blue arrow. The unit cell is indicated by a blue rectangle. (b) The bulk Brillouin zone and projected (001) surface Brillouin zone. (c) Corresponding (001) surface Brillouin zone. The dashed rectangle marks the momentum region covered in our ARPES measurements. (d) Fermi surface of ${\mathrm{WTe}}_2$ taken by ARToF-ARPES at 20 K with $p$-polarization geometry. The spectral weight distribution is obtained by integrating photoemission spectra at each momentum within an energy window of $[-2.5,2.5]$ meV with respect to the Fermi level. (e) Fermi surface of ${\mathrm{WTe}}_2$ taken by ARToF-ARPES at 20 K with $s$-polarization geometry. In both (d) and (e), the lower half region is obtained by symmetrizing the upper half part of the measured Fermi surface with respect to the $\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ mirror plane. (f) Schematic of all measured Fermi surface sheets. The solid lines represent the bulk pockets, and the dashed lines represent the surface state segments. Different pockets are drawn with different colors. (g) Calculated bulk Fermi surface at $k_z=0$. (h) Calculated projected Fermi surface including surface states. (i) Constant energy contours of ${\mathrm{WTe}}_2$ at different binding energies measured at 20 K under $p$-polarization geometry. (j) Same as (i) but measured under $s$-polarization geometry. All the images in this figure are obtained by the second derivative of the original data with respect to energy.

Figure 2

Band structures of ${\mathrm{WTe}}_2$ measured along typical momentum cuts and their comparison with the band structure calculations. (a) Fermi surface of ${\mathrm{WTe}}_2$ measured at 20 K under $p$-polarization geometry. The image is obtained by the second derivative of original data with respect to energy. (b) Band structures measured along different momentum cuts 1–5. The location of the five momentum cuts are marked by red lines in (a). The main bands are labeled in the cut 5 panel by lines with their colors corresponding to those of the Fermi pockets and surface state in Fig. 1. (c) Same as (a) but measured under $s$-polarization geometry. (d) Same as (b) but measured under $s$-polarization geometry. (e) Calculated bulk band structure along $X\text{−}\mathrm{\Gamma }\text{−}Y$ with $k_z$ at 0. (f) Calculated band structure along $\mathrm{\Gamma }\text{−}X$ including surface states. (g) Fermi surface of ${\mathrm{WTe}}_2$ measured at 20 K under $p$-polarization geometry. The image is obtained by the second derivative of original data with respect to energy. (h) Band structures measured along the momentum cuts marked in (g) as red lines. They show clear momentum evolution of the surface bands and the bulk bands. (i) Same as (g) but measured under $s$-polarization geometry. (j) Same as (h) but measured under $s$-polarization geometry.

Figure 3

Identification of Weyl points in ${\mathrm{WTe}}_2$ through its band structure evolution. (a) and (b) Band structures of ${\mathrm{WTe}}_2$ measured along different momentum cuts at 100 and 200 K. The location of the momentum cuts 1–5 are marked in (d). In order to observe electronic states above the Fermi level, the images in (a) and (b) are obtained by dividing the original data with the corresponding Fermi distribution function. W1 is the momentum space position of a “candidate Weyl point.” (c) The calculated band structures along the same five momentum cuts as marked in (d). (d) A schematic for the distribution of the calculated four sets of Weyl points within a bulk Brillouin zone at $k_z=0$: Weyl point 1 (W1) is represented by blue dots while Weyl point 2 (W2) by red dots. The chirality is marked with “+” and “$-$,” corresponding to $C=+1$ and $C=-1$. The Wilson loop is shown schematically as a pink solid curve. The locations of the five momentum cuts are marked by red lines where cut 2 crosses W1 Weyl point, cut 4 crosses W2 Weyl point, and cut 6 crosses both W1 and W2 Weyl points. (e) Expanded view of the region marked by the yellow rectangle in (c) for cut 2. Here, the electron band and hole band touch at the W1 Weyl point. (f). Expanded view of the region marked by the yellow rectangle in (c) for cut 4. Here, the electron band and hole band touch at the W2 Weyl point. (g) Calculated band structure for the momentum cut 6 that crosses the two Weyl points.

Figure 4

Identification of Weyl points in ${\mathrm{WTe}}_2$ through the constant energy contours. (a) and (b) Constant energy contours of ${\mathrm{WTe}}_2$ above the Fermi level measured at 100 and 200 K. The surface state SS1 is marked as the blue dashed line. Here, the 100 and 200 K data were taken from two separate ${\mathrm{WTe}}_2$ samples. W1 is the momentum space position of a “candidate Weyl point.” (c) Calculated constant energy contours of ${\mathrm{WTe}}_2$ including the surface state above the Fermi level near the Weyl points. The surface states SS1 and SS2 are marked by the yellow arrows. (d) Expanded view of the region crossing the W1 point marked by the yellow rectangle in (c) for the 56 meV energy. (e) Expanded view of the region crossing the W2 point marked by the yellow rectangle in (c) for the 89 meV energy. The W1 and W2 points are marked by the yellow arrows in (d) and (e).