Fig. 4: The calculated band structure and surface states of CoAs3, and the proposed mechanism of enhanced photocatalytic HER performance.

a Electronic band structure of CoAs3 considering the SOC. Insert: bulk Brillouin zones of CoAs3. b, c The enlarged view of the dashed red area for the enlarged band crossing points with and without SOC along the high symmetry path N–Γ–P in (a). The quadratic contact point at Γ above EF. (TCP triple contact-point, QCP quadratic contact-point, LS Luttinger semimetal). d, e Surface band structures of the top and down surfaces. Note, the trivial surface states are induced by unsaturated dangling bonds on the surface, where the surface states of Luttinger semimetal are clearly shown. f Color mapping of the calculated spin texture of Luttinger semimetal (LS) surface states. g Color plot of the calculated topological insulator (TI) surface states. h The proposed mechanism of enhanced visible light photocatalytic HER performance of CoAs3. Source data for Fig. 4 are provided as a Source data file.