Figure 1
Atomic and band structures of free-standing Cu₂Si. a Top and side view. The orange and blue balls represent Cu and Si atoms, respectively. b, c Calculated band structures of Cu₂Si without and with spin-orbit coupling (SOC), respectively. The vertical axis E-E _F corresponds to -E _B, where E _B is the binding energy. For simplicity, we label the three bands that cross the Fermi level α, β, and γ, respectively. The parity of mirror reflection symmetry for each band is labelled plus and minus signs in b. The zoom-in band structures in the blue and red ellipses are shown in g, h. d Band structure of Cu₂Si after artificially increasing the intrinsic SOC by 20 times. e Fermi surface of Cu₂Si without SOC. The blue, orange, and green lines correspond to bands α, β, and γ, respectively. f Momentum distribution of the nodal loops: NL1 (blue) and NL2 (orange). g, h Zoom-in band structures in the blue and red ellipses in c, which clearly show the SOC-induced gaps

Figure 2
ARPES results for monolayer Cu₂Si on Cu(111). a Schematic drawing of the Brillouin zones of Cu₂Si (blue hexagons) and Cu(111) (black hexagon). As the lattice of Cu₂Si is \left(\sqrt{3}\times \sqrt{3}\right)R30° with respect to the Cu(111)-1 × 1 lattice, the K point of Cu(111) is located at the Γ point of the second Brillouin zone of Cu₂Si. b–e Second derivative CECs measured using 30-eV p-polarized photons. Three closed contours have been observed: a hexagon, a hexagram, and a circle, as indicated by the dashed lines. f, i, j ARPES intensity plots along the Γ-K direction measured with different photon energies: 30, 35, and 25 eV, respectively. The black arrows mark the position of the crossing points. g, h ARPES intensity plots along the Γ-M direction measured with p and s polarized light, respectively. k ARPES intensity plots along the Γ-M direction measured with 60-eV circularly polarized light. The γ band is clearly observed while the α and β bands are suppressed