Figure 1

Comparison of theoretical results and experiment data [11] for the angle-integrated photoemission spectrum of silicon. The inset shows the spectral function of the lowest valence band at the $\Gamma$ point (${\Gamma }_{1v}$) in silicon from ab initio $GW$ (dashed blue curve) and ab initio $GW+C$ (solid red curve) theories. The energy is measured from the top of the valence band.Reuse & Permissions

Figure 2

(a) Comparison of ab initio $GW+C$, ab initio $GW$, and linear-band model $GW$ spectral functions at the Dirac point for isolated graphene with electron doping corresponding to a charge density $n=-12.4\times {10}^{13}{\mathrm{cm}}^{-2}$. Energies are measured relative to the Fermi energy. The inset shows an additional shoulderlike feature (indicated by arrow) in the ab initio $GW+C$ spectral function. (b) Imaginary part of the head of the interacting susceptibility (in a supercell calculation $\mathrm{Im}{\chi }_{00}(\mathit{q},\omega )=\mathrm{Im}{ϵ}_{00}^{-1}(\mathit{q},\omega )/v(\mathit{q})/n_g$ with $v(\mathit{q})$ denoting the truncated Coulomb interaction and $n_g$ the density of graphene sheets per unit length) for isolated graphene and for graphene on a SiC substrate. Note that $\mathrm{Im}{\chi }_{00}(\mathit{q},\omega )$ is proportional to the dynamical structure factor $S(\mathit{q},\omega )$ [27]. We also show the result from the linear-band model with a background dielectric of $\kappa (q_1)=2.2$. The results are for $n=-5.9\times {10}^{13}{\mathrm{cm}}^{-2}$ and $q_1=0.022\mathrm{a}.\mathrm{u}.$ The inset shows the background dielectric function $\kappa (q)$ used in the strictly 2D linear-band model for isolated graphene (solid circles), graphene on SiC (solid squares) and the cRPA result for isolated graphene obtained by Wehling et al. (solid line) [19].Reuse & Permissions

Figure 3

Comparison of ab initio $GW+C$ and GW spectral function (in 1/eV) for graphene on SiC at the Dirac point with experiment (experimental spectra are given in counts/second in arbitrary units) for (a) $n=-5.9\times {10}^{13}{\mathrm{cm}}^{-2}$ and (b) $n=-1.5\times {10}^{13}{\mathrm{cm}}^{-2}$. The arrows indicate the satellite position in the theoretical curves. The inset of (a) shows $\mathrm{Re}\delta \Sigma (\omega )-\omega +{ϵ}_{\mathrm{LDA}}$ with $\delta \Sigma =G_0^{-1}-G^{-1}$ for $GW$ (dark gray [blue] curve) and $GW+C$ (light gray [red] curve) as a function of $\omega$. The arrow denotes the plasmaron solution in $GW$, which does not exist in $GW+C$. The inset of (b) shows the geometry of graphene on a hydrogen-terminated 4H-SiC (0001) surface: carbon atoms are brown, silicon atoms are gray (blue) and hydrogens are white.Reuse & Permissions