Accurate selfenergy-corrections to local-density bands of semiconductors and insulators

The GW-approximation for the selfenergy 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 quasi-particle energies and wave functions, being also valid for the exact selfenergy. 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 selfenergies used within the LDA. The selfenergy and the dielectric response matrix are evaluated in plane wave representation. As far as the dynamics of the dielectric response is concerned a new generalized plasmon-pole concept for the dielectric matrix is used. We demonstrate that the wave functions obtained from the Empirical Pseudo-potential Method are sufficient to compute the final energy bands to within 0.1-0.2eV. Explicit results are given for germanium.