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

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Abstract

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.
Original languageEnglish
Pages (from-to)8351
Number of pages1
JournalPhysical Review / B
Volume37
Issue number14
DOIs
Publication statusPublished - 1988

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Wave functions
insulators
Semiconductor materials
Band structure
Local density approximation
wave functions
energy
Germanium
pseudopotentials
Computational efficiency
approximation
Poles
matrices
sum rules
energy bands
germanium
plane waves
poles
operators

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Precise quasiparticle energies and Hartree-Fock bands of semiconductors and insulators. / von der Linden, Wolfgang; Horsch, Peter.

In: Physical Review / B, Vol. 37, No. 14, 1988, p. 8351.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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