GW quasiparticle energy calculations for surfaces: the influence of polarization effects in a repeated-slab approach

The combination of density functional theory (DFT) and many-body perturbation theory in the \emph{GW} approximation has become an important tool for \emph{ab-initio} band structure calculations typically in good agreement with experiment. In order to treat surfaces one often employs a repeated slab geometry for computational convenience. However, electric multipole moments may occur in the slabs which then lead to a slowly decaying electrostatic interaction. If present, static dipoles must be corrected for in DFT [1]. In \emph{GW} however, dynamic dipoles are always created. We present calculations for the hydrogen-saturated silicon (001) slabs and show that slabs smaller than 10 layers are not converged fully with 10-20~\AA\ vacuum thickness. The effect of the dynamic dipoles is slowly decreasing with slab thickness, in accordance with an extension of a simple electrostatic model, that includes these polarization effects [2]. Therefore it is essential to monitor the convergence carefully and if necessary to extrapolate to infinite separation. \\ $[$1$]$ J. Neugebauer, M. Scheffler, Phys. Rev. B \textbf{46}, 16067 (1992) \\ $[$2$]$ C. Delerue, G. Allan and M. Lannoo, Phys. Rev. Lett. \textbf{90}, 076803 (2003)