Fig. 7: Physical origin iLDAD: momentum-dependent orbital orientation.

a Sketch of the calculated (TB + PW) iLDAD with labeled M/M' pockets (1–6). b Sketch of the hybrid orbital \({\widetilde{\psi }}_{m}({{{{{\bf{r}}}}}})\), for each M/M' points shown in (a). The orbital is represented by the constant-value contour \(| {\widetilde{\psi }}_{m}({{{{{\bf{r}}}}}})| =0.02\), while the red (blue) color shading indicates \({{{{{\rm{Re}}}}}}[{\widetilde{\psi }}_{m}({{{{{\bf{r}}}}}})] \, > \, 0\) (\({{{{{\rm{Re}}}}}}[{\widetilde{\psi }}_{m}({{{{{\bf{r}}}}}})] \, < \, 0\)). The coordinate systems corresponds to the laboratory frame. c projection of the hybrid orbitals onto the x–z plane. The photoelectron wave vector p is indicated by the black arrow.