LDA, GW, and exact-exchange Kohn-Sham scheme calculations of the electronic structure of sp semiconductors

Abstract

Electronic structures of Si, Ge, GaAs, BeSe, BeTe, MgSe, and MgTe resulting from the local-density approximation (LDA), exact-exchange (EXX) Kohn-Sham scheme and the many-body-GW approximation are compared. It is shown that although the EXX scheme gives good energy gaps between occupied and unoccupied bands, it underestimates by $\ensuremath{\sim}10%$ the widths of upper valence bands. The GW approximation is applied perturbatively either on top of the LDA, or EXX band structures in the zero order. It is argued that such a perturbative scheme carries a built-in ambiguity: the quasiparticle band structure depends on an arbitrary constant in the Kohn-Sham potential. This ambiguity could be removed by a requirement of the energy alignment between the Kohn-Sham and GW schemes.