Fig. 2. Observation of type II Weyl nodes in LaAlGe.

(A) High-energy soft x-ray ARPES (SX-ARPES) measurement and (B) first-principles calculation of k_z − k_x Fermi surface maps at k_y = 0. The dashed green hexagon in (A) and the black hexagon in (B) correspond to the boundary of the first BZ on the k_y = 0 plane. The photon energies corresponding to the k_z values in (A) are between 320 and 600 eV. (C) SX-ARPES–measured k_x − k_y Fermi surface map at k_y corresponding to the W₂ Weyl nodes. (D) Zoomed-in version of the measured and (E) calculated k_x − k_y Fermi surface maps in the region marked by the green rectangle in (C). In the first-principles calculations, blue lines correspond to hole-like pockets, whereas red lines indicate electron-like pockets. (F and G) Same as (D) and (E) for a constant energy contour at 25 meV below the Fermi level. The photon energy used in the measurements presented in (C), (D), and (F) is 542 eV. (G and H) First-principles–calculated k_x − k_y Fermi surface map at k_z = 0 (location of W₁, W₃′, and W₃″ Weyl nodes), which shows the shapes of the pockets resulting from W1, W₃′, and W₃″ and other trivial pockets. (I) SX-ARPES–measured k_x − k_y Fermi surface map at k_z = 0 in the region of the BZ denoted by the green dashed rectangle in (H). This experimentally observed Fermi surface map is in qualitative agreement with the calculated results presented in (H). The photon energy used here is 478 eV. (J) Calculated Fermi surface over the first bulk BZ. The pockets arising from the Weyl fermion cones are marked. Other pockets are trivial bulk bands. The red and blue colors denote electron- and hole-like pockets. Particularly, it can be seen that the W₂ node arises from the touching between electron and hole pockets, confirming their type II nature.