Precise quasiparticle energies and Hartree-Fock bands of semiconductors and insulators

The GW approximation for the self-energy operator is used to calculate the corrections to band structures obtained within the local-density approximation (LDA). To that end we derive rigorous expressions for the quasiparticle energies and wave functions, being also valid for the exact self-energy. A detailed analysis of the state and energy dependence of the nonlocal exchange-correlation contributions to the quasiparticle energies is given and compared to the approximative self-energies used within the LDA. The self-energy and the dielectric response matrix are evaluated in plane-wave representation. We demonstrate that the wave functions obtained from the empirical pseudopotential model (EPM) are sufficient to compute the final energy bands to within 0.1–0.2 eV. The merit of the EPM wave functions is a fast convergence and the possibility to calculate exchange-correlation self-energies for band structures which are determined in a localized basis. These wave functions incorporate all structural details contained in the ab initio wave functions. As far as the dynamics of the dielectric response is concerned a new generalized plasmon-pole concept for the dielectric matrix is introduced which fulfills all important sum rules and possesses the right analytical properties also for the off-diagonal elements. This new scheme provides a significant improvement in computational efficiency. Explicit results are given for germanium.