Fig. 4: Surface van Hove singularity near the Fermi energy.

a Ab-initio calculations (considering spin-orbit coupling) of the band structure projected onto the (001) surface, revealing the presence of surface states (SS), marked with arrows, and a van Hove singularity (vHs) at the \(\bar{{{{\rm{X}}}}}\) point. b Magnified view of the saddle point at the \(\bar{{{{\rm{X}}}}}\) point, marked with a red circle in panel (a). c Three-dimensional view of the surface state dispersion near the vHs at the \(\bar{{{{\rm{X}}}}}\) point on the k_x-k_y plane with k_z fixed at 0 Å. d Angle-resolved photoemission spectra (left column) and corresponding ab-initio calculations (considering spin-orbit coupling) illustrating the surface-projected constant energy contours at E_b = 0 eV,– 65 meV (where the vHs is located), − 100 meV, and 200 meV. For convenience, the coordinates of the \(\bar{{{{\rm{X}}}}}\) point are chosen to correspond to the (0, 0) coordinates. The photoemission spectroscopy results align with the calculated constant energy contours. The black arrow on the Fermi surface of the surface state indicates the location of the vHs, identified by the intersections among surface states. e Energy-momentum slices along the \(\bar{\Gamma }-\,\bar{{{{\rm{X}}}}}-\,\bar{\Gamma }\) and \(\bar{{{{\rm{S}}}}}-\,\bar{{{{\rm{X}}}}}-\,\bar{{{{\rm{S}}}}}\) directions acquired with photoemission spectroscopy (left column) and the (001) surface-projected calculation (right). The surface states (marked by white dashed parabolic bands) exhibit electron-like dispersion along \(\bar{\Gamma }-\,\bar{{{{\rm{X}}}}}-\,\bar{\Gamma }\) and hole-like dispersion along \(\bar{{{{\rm{S}}}}}-\,\bar{{{{\rm{X}}}}}-\,\bar{{{{\rm{S}}}}}\) the direction, forming a saddle point (marked by the black arrow) at the \(\bar{{{{\rm{X}}}}}\) point. For each binding energy, the energy-momentum cuts (panel e) are normalized at each binding energy to highlight band intensities near the Fermi level. The units in all the color bars shown are arbitrary units.