Figure 1

Photoemission intensity and theoretical results at different constant parallel momenta $k_{\overline{\Gamma }\overline{M}}$ along directions parallel to $\Gamma -Z$ (a) and constant normal momenta $k_z$ along directions parallel to $Z-U$ (b), which are shown by vertical and horizontal dashed lines in Fig. 2a, respectively. Dashed horizontal lines correspond to the experimentally observed energies of the VBM ($0.505\pm 0.030$ eV) and the CBM ($0.170\pm 0.025$ eV). The theoretical curves (shifted to have the VBM at the same energy as in the ARPES experiment) present the lowest conduction band and the uppermost valence band obtained for the experimental[25] (unrelaxed) and relaxed atomic positions without (LDA) and with (LDA+$GW$ or GGA+$GW$) the $GW$ corrections to the DFT (LDA or GGA) band structure. The two parallel and nearly vertical lines of higher photoemission intensity seen at $k_z$ values of roughly 2.8 and 3.0 ${\text{Å}}^{-1}$ in (a) correspond to Bi $5d$ core levels which have been excited by second-order light from the monochromator.Reuse & Permissions

Figure 2

(a) Contour plots of the lowest conduction band (upper row) and the uppermost valence band (lower row) in the mirror plane (see Fig. S1 of the Supplemental Material[26]) with the energy spacing of 0.05 eV between contour lines. The presented results are obtained for the experimental atomic positions without (LDA) and with (LDA+$GW$) the $GW$ corrections to the LDA band structure. Vertical and horizontal dashed lines drawn on the valence-band contour plot in the LDA+$GW$ case correspond to the cuts of the three-dimensional photon-energy scan, which are presented in Fig. 1. (b) Projections of the lowest conduction band and the uppermost valence band in the mirror plane on the $\overline{\Gamma }-\overline{M}$ direction of the two-dimensional BZ. The presented results are obtained for the experimental (upper row) and relaxed (lower row) atomic positions without (LDA) and with (LDA+$GW$) the $GW$ corrections to the LDA band structure. (c) Same as in (b), but without (GGA) and with (GGA+$GW$) the $GW$ corrections to the GGA band structure.Reuse & Permissions