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Cited by 3,963Advanced Chemical Physics StudiesPhysics of Superconductivity and MagnetismSurface and Thin Film Phenomena

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies

Hybertsen, Mark S., Louie, Steven G.·1986·Physical Review B
DOI 10.1103/physrevb.34.5390
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Abstract

We present a first-principles theory of the quasiparticle energies in semiconductors and insulators described in terms of the electron self-energy operator. The full dielectric matrix is used to evaluate the self-energy operator in the GW approximation: the first term in an expansion of the self-energy operator in terms of the dynamically screened Coulomb interaction (W) and the dressed Green's function (G). Quasiparticle energies are calculated for the homopolar materials diamond, Si, and Ge as well as for the ionic compound LiCl. The results are in excellent agreement with available experimental data. In particular, the indirect band gap is calculated as 5.5, 1.29, and 0.75 eV as compared with experimental gaps of 5.48, 1.17, and 0.744 eV for diamond, Si, and Ge, respectively. The Ge results include relativistic effects. The calculated direct gap for LiCl is within 5% of experiment. Viewed as a correction to the density-functional eigenvalues calculated with the local-density approximation, the present results show a correction dominated by a large jump at the gap. It is found that because of the charge inhomogeneity, the full dielectric screening matrix must be included, i.e., local-field effects are essential. The dynamical effects are also found to be crucial. The required dielectric matrices are obtained within the density-functional approach for the static case and extended to finite frequency with use of a generalized plasmon-pole model based on sum rules. The model reproduces the \ensuremath{\omega} and ${\ensuremath{\omega}}^{\mathrm{\ensuremath{-}}1}$ moments of the exact many-body response function. The qualitative features of the electron self-energy operator are discussed. Using the static Coulomb-hole--screened-exchange approximation for illustration, the role of local fields in the self-energy operator are explained. The role of dynamical renormalization is illustrated. The same qualitative features are observed in both the homopolar and ionic materials.

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  • For N, O, F and Hf, all the PSP libraries above perform less well in the Δ-factor test.

    “For a few selected elements, i.e. N, O, F and Hf, in which all the PSP libraries above perform less well in the ∆-factor test we also consider the recent NC Pseudo Dojo library [21] and, only for N, our own set (called THEOS) of US PSPs.”

    From Precision and efficiency in solid-state pseudopotential calculations (2018) · cites this paper as [21]

  • The SSSP efficiency and SSSP precision libraries (version 1.1) provide thoroughly tested and precise PSPs for 85 elements of the periodic table, selected from publicly available PSP libraries.

    “Leveraging the SSSP protocol, we identify two optimal PSP libraries, named SSSP efficiency and SSSP precision (version 1.1), that provide thoroughly tested and precise PSPs for 85 elements of the periodic table, selected from publicly available PSP libraries [16-22], for which the original authors should be acknowledged.”

    From Precision and efficiency in solid-state pseudopotential calculations (2018) · cites this paper as [21]

  • Using the SSSP protocol, the authors identify two optimal PSP libraries, named SSSP efficiency and SSSP precision (version 1.1).

    “Leveraging the SSSP protocol, we identify two optimal PSP libraries, named SSSP efficiency and SSSP precision (version 1.1), that provide thoroughly tested and precise PSPs for 85 elements of the periodic table, selected from publicly available PSP libraries [16-22], for which the original authors should be acknowledged.”

    From Precision and efficiency in solid-state pseudopotential calculations (2018) · cites this paper as [21]

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Authors
Hybertsen, M. S., & Louie, S. G.
Affiliations
University of California, Berkeley (US)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1986-10-15
Volume
34
Issue
8
Pages
5390-5413
ISSN
0163-1829 (ISSN-L)
DOI
10.1103/physrevb.34.5390
OpenAlex
W2014094922
Cited by
3,963
References
81
Citations by year
2026: 172 · 2025: 205 · 2024: 184 · 2023: 184 · 2022: 188 · 2021: 217 · 2020: 185 · 2019: 161 · 2018: 162 · 2017: 160 · 2016: 173 · 2015: 167 · 2014: 152 · 2013: 114 · 2012: 121
FWCI
26.74
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B, Condensed matter (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
Keywords
electron correlation, quasiparticle energies, GW approximation, band gap, indirect band gap, local field effects, sum rules, dynamical screening, diamond, silicon, germanium, lithium chloride, local density approximation, relativistic effects

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