Fig. 1: Crystal structure, WPs and calculated electronic structure of CrSb.
a The crystal structure of CrSb with the space group P63/mmc (no. 194). b The 3D BZ of the original unit cell of CrSb, and the corresponding two-dimensional BZ projected on the (001) plane (green lines). The red, green, blue, and orange planes are the four mirror planes in the BZ on which the altermagnetic bands are spin-degenerate in absence of SOC. c Calculated bulk Fermi surface in the first BZ. The colormap from blue to orange of Fermi surface sheet represents the expectation value of spin along the z direction. Illustration of the two types of WPs: opposite-spin (d) and same-spin (e). The yellow, red, and blue lines connecting WPs are surface Fermi arcs (SFAs). The purple lines represent spin-up and spin-down degeneracy. Top (f) and side (g) views of the distribution of same-spin WPs in the 3D BZ. Red dots represent nodes with chirality χ = +1, green dots χ = −1. The calculated surface state of (001) on Sb (h) and Cr (i) terminations along \({\overline{{\rm{M}}}}_{1}-\overline{\Gamma }-{\overline{\rm{M}}}_{2}-{\overline{\rm{K}}}_{2}-\overline{\Gamma }-{\overline{\rm{K}}}_{1}-{\overline{\rm{M}}}_{1}\). The WPs are marked by the red (χ = 1) and green (χ = −1) dots. Star, square and round dots represent the projected positions of opposite-spin WPs on the high symmetry line/plane (WP1), opposite-spin WPs on general momenta (WP2) and same-spin WPs (WP3), respectively.
