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.