Quasi-particle band structures and optical properties of the "magic sequence" SiGe superstructure

The quasi-particle band structure and dielectric function for the so-called magic sequence SiGe$_2$Si$_2$Ge$_2$SiGe$_{12}$ (or $\alpha_{12}$) structure [PRL 108, 027401 (2012)] are calculated by many-body perturbation theory (MBPT) within an ab-initio framework. On top of density functional calculations within the local density approximation (LDA) leading to a fundamental band gap of 0.23 eV, we have computed the quasi-particle band structure within the G$_0$W$_0$ approach opening the gap to 0.61 eV. Moreover, we have calculated the optical properties by solving the Bethe-Salpeter equation (BSE) for the electron-hole two-particle correlation function. When comparing the imaginary part of the dielectric function obtained at various levels of approximation, \emph{i.e.} the independent particle approximation (or random phase approximation) based on (i) the LDA or (ii) GW band structures, and (iii) the BSE including local field effects and electron-hole correlations, we observe that the important first transition is better explained with taking into account excitonic effects. Moreover, the onset transition originating from the direct transition of the magic sequence structure is also investigated.