Extended Data Fig. 1: First-principles calculations and angle-resolved photoemission spectroscopy determination of the electronic band structures.

a, First Brillouin zone and the projected surface along (111). Note that L is part of a group of three inequivalent L-points that are related by C₃ rotation symmetry around the z-axis. In the caption of Fig. 4 and the Supplementary Information, these are referred to as L, L′, and L″. b, Electronic band structure of bulk α-As calculated using density functional theory over the whole bulk Brillouin zone, taking into consideration the presence of spin-orbit coupling. The bands crossing the Fermi energy are highlighted in magenta (valence band) and cyan (conduction band). c, Left: Calculated surface bands connecting the conduction and valence bands with Rashba-like features. These bands, depicted using bright orange curves, are projected on the (111) surface (also shown in Fig. 1g). Right: Calculated spin texture of the Rashba-like surface bands. d-f, Angle-resolved photoemission spectroscopy energy-momentum cuts encompassing high symmetry points- \(T\) (panel d), \(\varGamma \) (panel e), and \({L}_{3}\) (panel f)- of the bulk Brillouin zone. The directions are marked in panel a with dashed blue lines. The cuts are measured with a linear -horizontal polarized light with the photon energies of 67 eV (panel d), 40 eV (panel e), and 97 eV (panel f), respectively. The right panels in d-f show the corresponding band structures obtained via first-principles calculations. The bulk bands obtained from photoemission spectroscopy qualitatively match the first-principles results. g, Constant energy contour of the photon energy dependence measurement at the Fermi energy. The size of the electron pocket near \(\varGamma \) does not depend on the photon energy, which confirms its surface-state nature. h, Energy-momentum cut (left) and its second derivative (right) taken along \(\bar{\varGamma }-\bar{M}\) direction of the surface Brillouin zone, obtained from photoemission spectroscopy on the cleaved (111) surface (ab plane). The spectra were acquired using 22 eV, linear-horizontally polarized light. The topological surface state is marked by the white arrow. The small Rashba splitting is visualized in the second derivative plot (also shown in Fig. 1f). i, Extracted dispersion of the Rashba-split surface states, shown using red and blue points. Red and blue curves denote parabolic fits to the photoemission data. These photoemission spectroscopy results are consistent with the first-principles calculations presented in panel c.