Three-Dimensional Electronic Structure of the Type-II Weyl Semimetal ${\mathrm{WTe}}_2$

By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of ${\mathrm{WTe}}_2$, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the $\mathrm{\Gamma }$ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of ${\mathrm{WTe}}_2$ around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

Figure 1

(a) View of the ${\mathrm{WTe}}_2$ crystal structure. W and Te atoms are shown in orange and blue, respectively. (b) Relative bulk and (001) surface Brillouin zones. (c) $k_x\text{−}{k}_z$ Fermi surface ($k_y=0$) taken in the 400–800 eV range of excitation energies. The value of the inner potential $V_0=-6.5\mathrm{eV}$ is used to compute the $k_z$ periodicity over many Brillouin zones (see rectangles), assumed here to be $2\pi /c\sim 0.45{\AA }^{-1}$; see main text for a discussion. (d)–(f) $E$ vs $k$ band dispersions along the blue dashed lines in (c). Arrows are guides to the eyes to highlight features from the hole and electron pockets in a way consistent with (c). (g) Enlargement of the $k_x\text{−}{k}_z$ Fermi surface around the ${\mathrm{\Gamma }}_{30}$ point [red rectangle in (c)], and (h)–(i) calculated Fermi surface within the LDA and $\mathrm{LDA}+U$ ($U=2\mathrm{eV}$) approximations.

Figure 2

$k_x\text{−}{k}_y$ Fermi surfaces recorded with (a) UV ARPES at $h\nu =68\mathrm{eV}$ ($k_z=4.3{\AA }^{-1}$) and (b) soft-x-ray ARPES at $h\nu =425\mathrm{eV}$ ($k_z=10.8{\AA }^{-1}$), respectively. Green solid lines are reproduced from Ref. [35], corresponding to the extremal orbits with the areas determined from quantum oscillation measurements. (c) Calculated $k_x\text{−}{k}_y$ bulk Fermi surface within the $\mathrm{LDA}+U$ approximation for $U=2\mathrm{eV}$.

Figure 3

(a)–(b) $\mathrm{LDA}+U$ band structures for $U=0.0$ and 2.0 eV along the $k_x$ direction, respectively. The red box in panel (b) refers to the zoom area in (c) where the 3D linear band crossing (see arrow) occurs at finite $k_y=\pm 0.0045{\AA }^{-1}$ for $U$ values smaller than the critical $U_c=1.98\mathrm{eV}$. (d) GW band structure (solid red) as compared to the LDA (dot-dashed black).