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Exchange — Correlation Potential for the Quasi-Particle Bloch States of a Semiconductor

  • W. Hanke
  • N. Meskini
  • H. Weiler

Abstract

A summary is given of recent investigations we have performed on a) the interrelation of many-body perturbation theory for the non-local and energy-dependent self-energy and the density-functional theory, b) the single-particle-like excitations in Si which are calculated within the time-dependent screened Hartree-Fock (TDSHF) approximation, and c) an analytical energy- and local-density (ρ1/3-) dependent model for the self-energy of nonmetallic systems in general.

We elaborate on recent attempts to derive the local and energy-dependent density-functional potential vxc from the diagrammatic structure of many-body perturbation theory for the exact exchange-correlation energy, without explicit recourse to an extremal principle. The local vxc can be related to the nonlocal and dynamic self-energy Σ obtained from perturbation theory.

We summarize our recent calculations of quasiparticle states in silicon which aim at a first-principle understanding of the self-energy corrections in a prototype semiconductor. TDSHF is used by replacing the exchange operator by a dynamically screened interaction. In contrast to previous calculations in semiconductors the wave-vector and frequency-dependent two-particle propagator is calculated from first principles and includes local-field and particle-hole (excitonic) effects. The band gap, the valence-band width and the general features of quasiparticle decay are in good accord with experiment, though our construction of bare HF states via a density matrix built from pseudopotential eigenstates puts limits on this comparison.

On the basis of these numerical results, we outline the construction of an analytic, energy-dependent and local density-dependent model for the self-energy operator. This tight-binding model reproduces the computational results for dynamical self-energies in both the insulator C and semiconductor Si within a few percent across valence and conduction bands. The strength of the self-energy scales with ρ1/3. In particular, it is shown how the intrinsi- cally non-local (due to long-range electron-hole polarizations) potential can still approximately be converted via a Lorentz-sphere construction into a local potential. Together with the perturbation-theoretical expression for the “exact” vxc of density-functional theory this tight-binding model is finalY used to derive a model expression for vxc of a non-metal.

Keywords

Dyson Equation Quasiparticle State Plasmon Pole Bare Coulomb Interaction Quasiparticle Decay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L.J. Sham and W. Kohn, Phys. Rev. 145: 561 (1966)CrossRefGoogle Scholar
  2. 2.
    G. Baym, Phys. Rev. 127: 1391 (1962)Google Scholar
  3. 3.
    L. Hedin and S. Lundqvist, Solid State Phys. Vol. 23 (Academic N.Y.) 1969 pp.1, and references therein; L. Hedin, Phys. Rev. 139: A796 (1965)Google Scholar
  4. 4.
    W. Hanke and L.J. Sham, Phys. Rev. Lett. 43: 387 (1979); Phys. Rev. B21: 4656 (1980)CrossRefGoogle Scholar
  5. 5.
    G. Strinati, H.J. Mattausch and W. Hanke, Phys. Rev. Lett. 45: 290 (1980), Phys. Rev. B25: 2867 (1982)Google Scholar
  6. 6.
    W. Hanke, G. Strinati and H.J. Mauttausch, in “Recent Developments in Condensed Matter Physics”, Vol. 1, ed. by J.T. Devreese (Plenum, 1981), p.p. 263Google Scholar
  7. 7.
    P. Hohenberg and W. Kohn, Phys. Rev. 136: B864 (1964)CrossRefGoogle Scholar
  8. 8.
    W. Kohn and L.J. Sham, Phys. Rev. 140: A1133 (1965); for recent developments see also O. Gunnarson, M. Jonson and B.I. Lundqvist, Phys. Rev. B20: 3136 (1979), and A.R. Williams, U.v. Barth in “Theory of the Inhomogeneous Electron Gas” ed. by S. Lundqvist and N.H. March (Plenum, 1983 )Google Scholar
  9. 9.
    O. Gunnarson and R.O. Jones, Phys. Scr. 21: 394 (1980)Google Scholar
  10. 10.
    V.L. Moruzzi, J.F. J.anak and A. R. Williams, in “Calculated El-Electronic Properties of Metals” ( Pergamon, Oxford, 1978 )Google Scholar
  11. 11.
    D. Glötzel, B. Segall and O.K. Andersen, Sol. State Comm. 36: 403 (1980)Google Scholar
  12. 12.
    M.T.Yin and M.L. Cohen, Phys.Rev. B26: 5668 (1982)Google Scholar
  13. 13.
    L.J.Sham and M. Schlüter, Phys. Rev. Lett. 51: 1888 (1983)Google Scholar
  14. 14.
    D.C. Langreth, to be publishedGoogle Scholar
  15. 15.
    W. Hanke, T.Gölzer and H.J. Mattausch, Sol. State Comm. (1984), and Phys. Rev. B to be publishedGoogle Scholar
  16. 16.
    W. Hanke, H.J. Mattausch and G. Strinati, in “Electron Correlations in Solids,Molecules and Atoms”, ed. by J.T. Devreese and F. Brosens (plenum, 1983), p.p. 289Google Scholar
  17. 17.
    C.S. Wang and W.E. Picklett, Phys. Rev. Lett. 51: 597 (1983)Google Scholar
  18. 18.
    S. Horsch, P. Horsch and P. Fulde, Phys. Rev. B29: 1870 (1984)Google Scholar
  19. 19.
    J. C. Slater, Phys. Rev. 81: 385 (1951)Google Scholar
  20. 20.
    L. Ley, M. Cardona and R.A. Pollak, in “Photoemission in Solids” ed. by L. Ley and M. Cordona ( Springer, Berlin 1979 ),p. 11Google Scholar
  21. 21.
    This LDA “Hartree” calculation was provided by C. Kunc; independently very similar results were found by D. Glötzel.Google Scholar
  22. 22.
    HF results for MgO: S.T. Pantelides, D. J. Mickish and A.B. Kunz Phys. Rev. B10: 5203 (1974), and B10: 2602 (1974)Google Scholar
  23. 23.
    HF results for C:A. Mauger and M. Lannoo, Phys. Rev. B15:2324 (1977)Google Scholar
  24. 24.
    LDA for Si:D.R. Hamann, Phys. Rev. Lett.42:662 (1979)Google Scholar
  25. 25.
    LDA for C: A. Zunger and A.J. Freeman, Phys. Rev. B15:5049(1977)Google Scholar
  26. 26.
    J.P.Perdew and M. Levy, Phys. Rev. Lett. 51: 1884 (1983)Google Scholar
  27. 27.
    J.P. Perdew and A. Zunger, Phys. Pev.B23:5048 (1981), and references therein; R. E. Heaton, J.G. Harrison and C.C. Lin, Phys. Rev. B28: 5992 (1983)Google Scholar
  28. 28.
    J.D. Talman and W.F. Shadwick, Phys. Rev. A14: 36 (1976)Google Scholar
  29. 29.
    G. Baym and L.P. Kadanoff, Phys. Rev. 124: 287 (1961)Google Scholar
  30. 30.
    W. Kohn and P. Vashista, in “Theory of the Inhomogeneous Electron Gas”, ed. by S. Lundqvist and N.H. March, (Plenum, N.Y., 1983) eq. (168)Google Scholar
  31. 31.
    N.D. Mermin, Phys. Rev. 137A: 1441 (1965)Google Scholar
  32. 32.
    L.J. Sham and T.M. Rice, Phys. Rev. 144: 708 (1966)Google Scholar
  33. 33.
    W. Hanke and L.J. Sham, Phys. Rev. B12: 4501 (1975)Google Scholar
  34. 34.
    W. Hanke in “Festkörperprobleme XIX”, Adv. Sol. St. Phys.(Vieweg, (1979) p.p.43Google Scholar
  35. 35.
    H.J. Mattausch, W. Hanke and G. Strinati, Phys. Rev. B27: 3735 (1983)CrossRefGoogle Scholar
  36. 36.
    N. Meskini, H.J. Mattausch and W. Hanke, Sol. St. Comm. 48: 807 (1983)CrossRefGoogle Scholar
  37. 37.
    J.C. Slater, in The Self-Consistent Field for Molecules and Solids“, Vol. 4 (Mc-Graw-Hill, 1974) p.p.26Google Scholar
  38. 38.
    J.W.D. Conolly, “The X 0 Method”, Modern Theoret. Chem. 7 G.A. Segal ed. (Plenum, 1979); Ch.4Google Scholar
  39. 39.
    E.O. Kane, Phys. Rev. B4: 1910 (1971)CrossRefGoogle Scholar
  40. 40.
    W. Brinkman and B. Goodman, Phys. Rev. 149: 597 (1966)Google Scholar
  41. 41.
    N.O. Lipari and W.B. Fowler, Phys. Rev. B2: 3354 (1970)Google Scholar
  42. 42.
    J. Bennett and J.C. Inkson, J. Phys. C10: 987 (1977)Google Scholar
  43. 43.
    E.O. Kane, Phys. Rev. B5:1493 (1972) and C11: 2017 (1978)Google Scholar
  44. 44.
    J.R. Chelikowsky and M.L. Cohen, Phys. Rev. B10: 5095 (1974)Google Scholar
  45. 45.
    M. Cardona, in. Cardona, in “Atomic Struct.a. Propert. of Solids” (Academic, 1972 )Google Scholar
  46. 46.
    ß.I. Lundqvist, Phys. Condens. Matter 6; 193 (1967)Google Scholar
  47. 47.
    J.C. Slater, Phys. Rev. 81: 385 (1951)Google Scholar
  48. 48.
    P. Sterne and J.C. Inkson, J. Phys. C17: 1497 (1984)Google Scholar
  49. 49.
    R.N. Euwema, G.G. Wepfer, G.T. Surralt and D.L. Wilhite, Phys. Rev. B9: 5249 (1974)CrossRefGoogle Scholar
  50. 50.
    P. Horsch, to be published; and K.P. Bohnen, private communicationGoogle Scholar
  51. 51.
    C.S. Wang, B.M.Klein, Phys. Rev. B24: 33–93 (1981)Google Scholar
  52. 52.
    F. Manghi, G. Riegler, C.M. Bertoni, C. Calandra, G.B. Bachelet Phys. Rev. B28: 61–57 (1983)Google Scholar
  53. 53.
    A. Zunger, A.J. Freeman, Phys. Rev. B16:29O1 (1977)Google Scholar
  54. 54.
    From “Physics Data” 8–1 (1977), DESY Hamburg, edited by E.E. KochGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • W. Hanke
    • 1
  • N. Meskini
    • 1
    • 2
  • H. Weiler
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80The Federal Republic of Germany
  2. 2.Faculté des Sciences, Departement de PhysiqueCampus UniversitaireBelvédère, TunisTunisia

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