Local Density Functional and Strong On-Site Correlations: The Electronic Structure of La2CuO4

  • M. T. Czyżyk
  • G. A. Sawatzky
Part of the NATO ASI Series book series (NSSB, volume 337)


The density functional (DF) theory has been a most successful theoretical method for describing ground state properties in solid state physics since the beginning of seventies [1, 2]. An enormous amount of applications of the local density approximation (LDA) to the DF can be found in the literature for the description of a wide range of phenomena in a wide range of materials (see e.g. references within Refs. [1, 2] and reviews [3, 4]). Unfortunately the class of materials where the LDA does not work properly is also growing rapidly including those with the most startling physical properties.


Local Density Approximation Unoccupied State Lower Hubbard Band Slater Integral Apex Oxygen 
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  1. [1]
    Theory of the Inhomogeneous Electron Gas edited by S. Lundqvist and N.H. March, (Plenum, 1983).Google Scholar
  2. [2]
    G.D. Mahan and K.R. Subbaswamy, Local Density Theory of Polarizability, (Plenum, 1990).Google Scholar
  3. [3]
    R.O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).ADSCrossRefGoogle Scholar
  4. [4]
    W.E. Pickett, Rev. Mod. Phys. 62, 433 (1989).ADSCrossRefGoogle Scholar
  5. [5]
    D.C. Langreth and J.P. Perdew, Phys. Rev. B21, 5469 (1980).ADSGoogle Scholar
  6. D.C. Langreth and M. J. Mehl, Phys. Rev. B28, 1809 (1983).ADSGoogle Scholar
  7. J.P. Perdew and Y. Wang, Phys. Rev. B33, 8800 (1986).ADSGoogle Scholar
  8. [6]
    J.P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981).ADSGoogle Scholar
  9. [7]
    J.P. Perdew in Advances in Quantum. Chemistry, Vol. 21, edited by S.B. Trickey, p. 113 (Academic Press, 1990), and the references therein.Google Scholar
  10. [8]
    V.I. Anisimov, J. Zaanen, and O.K. Andersen, Phys. Rev. B44, 943 (1991).ADSGoogle Scholar
  11. [9]
    J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Jr, Phys. Rev. Lett. 49, 1691 (1982).ADSCrossRefGoogle Scholar
  12. [10]
    A.R. Williams, J. Kübier, and C.D. Gelatt, Jr, Phys. Rev. B19, 6094 (1979).ADSGoogle Scholar
  13. [11]
    M.T. Czyżyk, R.A. de Groot, G. Dalba, P. Fornasini, A. Kisiel, F. Rocca, and E. Burattini, Phys. Rev. B39, 9831 (1989).ADSGoogle Scholar
  14. J. Ghijsen, L.H. Tjeng, J. van Elp, H. Eskes, J. Westerink, G.A. Sawatzky, and M.T. Czyżyk, Phys. Rev. B38, 11322 (1988).ADSGoogle Scholar
  15. M. Grioni, M.T. Czyżyk, F.M.F. de Groot, J.C. Fuggle, and B.E. Watts, Phys. Rev. B39, 4886 (1989).ADSGoogle Scholar
  16. M.T. Czyżyk, and R.A. de Groot, in Proceedings of the Second European Conference on Progress in X-ray Synchrotron Radiation Research Research, Rome, Italy 1989, edited by A. Balerna, E. Bernieri, and S. Mobilio, (Italian Physical Society, Bolonia 1990), p.47.Google Scholar
  17. P.J.W. Weijs, M.T. Czyżyk, J.F. van Acker, W. Speier, J.B. Goedkoop, H. van Leuken, H.J.M. Hendrix, R.A. de Groot, G. van der Laan, K.H.J. Buschow, G. Wiech and J.C. Fuggle, Phys. Rev. B41, 11899 (1990).ADSGoogle Scholar
  18. [12]
    H. van Leuken, A. Lodder, M.T. Czyżyk, F. Springelkamp, and R.A. de Groot, Phys. Rev. B41, 5613 (1990).ADSGoogle Scholar
  19. [13]
    M.T. Czyżyk, K. Lawniczak-Jabloriska, and S. Mobilio, Phys. Rev. B45, 1581 (1992);.ADSGoogle Scholar
  20. [14]
    M.T. Czyżyk, R. Potze, and G.A. Sawatzky, Phys. Rev. B46, 3729 (1992).ADSGoogle Scholar
  21. [15]
    O.K. Andersen, Phys. Rev. B12, 3060 (1975).ADSGoogle Scholar
  22. H.K. Skriver, The LMTO Method, (Berlin, 1984).Google Scholar
  23. [16]
    O.K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, 2571 (1984).ADSCrossRefGoogle Scholar
  24. [17]
    E.U. Condon and G.H. Shortley, The Theory of Atomic Spectra, (Cambridge, 1953).Google Scholar
  25. [18]
    J.S. Griffith, The Theory of Transition-Metal Ions, (Cambridge, 1961).Google Scholar
  26. [19]
    A.M. Oles and G. Stollhoff, Phys. Rev. B29, 314 (1984).ADSGoogle Scholar
  27. [20]
    J.B. Grant and A.K. McMahan, Phys. Rev. B46, 8440 (1992).ADSGoogle Scholar
  28. [21]
    M.M. Steiner, R.C. Albers, and L.J. Sham, Phys. Rev. B45, 13272 (1992).ADSGoogle Scholar
  29. [22]
    V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyżyk, and G.A. Sawatzky, to appear in Phys. Rev. B. (Dec.‘93).Google Scholar
  30. [23]
    A.K. McMahan, R.M. Martin, and S. Satpathy, Phys. Rev. B38, 6650 (1988).ADSGoogle Scholar
  31. [24]
    O. Gunnarsson, O.K. Andersen, O. Jepsen, and J. Zaanen, Phys. Rev. B39, 1708 (1989).ADSGoogle Scholar
  32. [25]
    M.S. Hybertsen, and M. Schlüter, Phys. Rev. B39, 9028 (1989).ADSGoogle Scholar
  33. [26]
    A.K. McMahan, J.F. Annett, and R.M. Martin, Phys. Rev. B42, 6268 (1990).ADSGoogle Scholar
  34. [27]
    One should be a bit careful when comparing the values of U reported in the literature, because of the different, often only implicitly assumed conventions which are used. All values obtained by constrained-LDA calculations involving atomic-sphere (muffin-tin) approximation should be identified with screened Slater monopole integral F 0 eff. So we do, see Appendix. The diagonal values of Coulomb interaction U mm, m = x 2y 2, 3z 2r 2,xy, etc, are, however, different. In terms of Racah A, B and C parameters they read: U d = F 0 eff., A + 7/5C, and U mm = A + 4B + 3C. As an example, U d = 7.42 eV in Ref. [26] and U(d x 2y 2) = 8.96 eV in Ref. [20] are in fact the same. Of course, values of B and C have to be known. The authors of references used in this example did not confuse that matter, but it seems that ambiguity about these values exists in the literature.Google Scholar
  35. [28]
    V.I. Anisimov, M.A. Korotin, J. Zaanen, and O.K. Andersen, Phys. Rev. Lett. 68, 345 (1992).ADSCrossRefGoogle Scholar
  36. [29]
    V.l. Anisimov, private communication.Google Scholar
  37. [30]
    C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand. (U.S.), No. 467 (Washington, D.C. 1958), Vols. 1-3.Google Scholar
  38. [31]
    H. Eskes, L.H. Tjeng, and G.A. Sawatzky, Phys. Rev. B41, 288 (1990).ADSGoogle Scholar
  39. [32]
    H. Eskes, and G.A. Sawatzky, Phys. Rev. B44, 9656 (1991).ADSGoogle Scholar
  40. [33]
    F.M.F. de Groot, J.C. Fuggle, B.T. Thole, and G.A. Sawatzky, Phys. Rev. B42, 5459 (1990).ADSGoogle Scholar
  41. [34]
    J.B. Mann, Atomic structure calculations, Los Alamos Scientific Laboratory Reports No.LASL-3690 (1967).Google Scholar
  42. [35]
    S.L. Cooper, G.A. Thomas, A.J. Millis, P.E. Sulewski, J. Orenstein, D.H. Rapkine, S-W, Cheong, and P.L. Trevor, Phys. Rev. B42, 10785 (1990).ADSGoogle Scholar
  43. [36]
    J. Zaanen, G.A. Sawatzky, and J.W. Allen, Phys. Rev. Lett. 55, 418 (1985).ADSCrossRefGoogle Scholar
  44. [37]
    F. Barriquand, and G.A. Sawatzky, submitted to Phys. Rev. B.Google Scholar
  45. [38]
    E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).ADSCrossRefGoogle Scholar
  46. [39]
    Y. Gao, T.J. Wagener, J.H. Weaver, A.J. Arko, B. Flandermeyer, D.W. Capone II, Phys. Rev. B36, 3971 (1987).ADSGoogle Scholar
  47. [40]
    F.C. Zhang, and T.M. Rice, Phys. Rev. B37, 3759 (1988).ADSGoogle Scholar
  48. [41]
    E. Pellegrin, N. Nücker, J. Fink, S.L. Molodtsov, A. Gutierrez, E. Navas, O. Strebel, Z. Hu, M. Domke, G. Kaindl, S. Uchida, Y. Nakamura, J. Markl, M. Klauda, G. Saemann-Ischenko, A. Krol, J.L. Peng, Z.Y. Li, and R.L. Greene, Phys. Rev. B47, 3354 (1993). The experimental spectra presented in Fig. 6 differ slightly from those published by Pellegrin et al. We used spectra which were corrected for the self-absorption effect and which were kindly provided to us by E. Pellegrin after publication.Google Scholar
  49. [42]
    C.T. Chen, L.H. Tjeng, J. Kwo, H.L. Kao, P. Rudolf, F. Sette, and R.M. Fleming, Phys. Rev. Lett. 68, 2543 (1992).ADSCrossRefGoogle Scholar
  50. [43]
    We used such a broadening procedure successfully in many occasions. See e.g. Ref. [11, 13] and [14].Google Scholar
  51. [44]
    Such an expectation is based on our previous experience with self-consistent calculations of the core-hole effects on the XAS spectra in semiconductors and metals. See: M.T. Czyżyk, and R.A. de Groot, Proc. of ”2nd European Conf. on Progress in X-ray Synchrotron Radiation Research, p. 47, Rome, Italy, October 1989; P.J.W. Weijs, M.T. Czyèyk, J.F. van Acker, W. Speier, J.B. Goedkoop, H. van Leuken, H.J.M. Hendrix, R.A. de Groot, G. van der Laan, H.J. Buschow, G. Wiech, J.C. Fuggle, Phys. Rev. B41, 11899 (1990).ADSGoogle Scholar
  52. [45]
    Z-X. Shen, J.W. Allen, J.J. Yeh, J.-S. Kang, W. Ellis, W. Spicer, I. Lindau, M.B. Maple, Y.D. Dalichaouch, M.S. Torikachvili, J.Z. Sun, and T.H. Geballe Phys. Rev. B36, 8414 (1987).ADSGoogle Scholar
  53. [46]
    A. Fujimori, E. Takayama-Muromachi, Y. Uchida, and B. Okai, Phys. Rev. B35, 8814 (1987).ADSGoogle Scholar
  54. [47]
    J. Ghijsen, L.H. Tjeng, J. van Elp, H. Eskes, J. Westerink, G.A. Sawatzky, and M.T. Czyżyk, Phys. Rev. B38, 11322 (1988).ADSGoogle Scholar
  55. [48]
    H. Eskes and G.A. Sawatzky, Phys. Rev. Lett. 61, 1415 (1988).ADSCrossRefGoogle Scholar
  56. [49]
    J.A. Gaunt, Phil.Trans. A. 228, 151 (1929).ADSzbMATHCrossRefGoogle Scholar
  57. [50]
    D.A. Varshslovich, A.N. Moskalev, and V.K. Khersonskii, Quantum Theory of Angular Momentum, (World Scientific, 1989).Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • M. T. Czyżyk
    • 1
  • G. A. Sawatzky
    • 1
  1. 1.Department of Solid State and Applied PhysicsUniversity of GroningenAG GroningenThe Netherlands

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