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Relativistic electronic structure of the Pb (001) surface

Abstract

The surface electronic band structure of the Pb (001) was calculated using the self-consistent, first-principles linear-augmented-plane-wave method and the norm-conserving pseudopotentiai method. In the nonrelativistic case, forbidden gaps appear above and below the Fermi levelin the bulk projected band structure of lead. An occupied surface state at the\(\overline M \) point and two surface states in a wide forbidden gap above EF are found. A characteristic feature of the electronic structure of the Pb (001) surface is the absence of a surface state within the forbidden S-P gap in the vicinity of the\(\overline \Gamma \) point. The inclusion of scalar-relativistic effects leads to the merger of several S-P gaps into one wide gap extending throughout the entire Brillouin zone. At the same time, the occupied state at point\(\overline M \) extends to point\(\overline X \) and its energy decreases by 2 eV. New, relatively weak surface states in the\(\overline {XM} \) direction and unoccupied states in the vicinity of the\(\overline \Gamma \) point appear. An unoccupied surface state is found at the bottom of the forbidden gap at point\(\overline M \). Including the contribution of the spinorbit pseudopotentiai leads to the appearance of two-spin orbit gas; however, the surface level structure is practically unchanged (except for the disappearance of the unoccupied surface state of Pz-symmetry at point\(\overline M \)).

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Literature cited

  1. 1.

    S. D. Kevan, N. G. Stoffel, and N. V. Smith, Phys. Rev.,B32, 4956 (1985).

  2. 2.

    P. L. Wincott, N. B. Brooks, D. S. L. Law, and G. Thornton, Phys. Rev.,B33, 4373 (1986).

  3. 3.

    T. S. Padmore, G. Thornton, and H. A. Padmore, Solid State Commun.,67, 163 (1988).

  4. 4.

    B. Schmiedeskamp, B. Kessler, N. Muiler, et al., Solid State Commun.,65, 665 (1988).

  5. 5.

    K. Zeong, R. H. Gaylord, and S. D. Kevan, Phys. Rev.,B38, 10302 (1988).

  6. 6.

    R. H. Gaylord and S. D. Kevan, Phys. Rev.,B36, 9337 (1987).

  7. 7.

    G. Jezequel, Y. Petroff, R. Pinchaux, and F. Yndurain, Phys. Rev.,B33, 4352 (1986).

  8. 8.

    M. Steslicka and S. G. Davison, Phys. Rev.,B1, 1958 (1970).

  9. 9.

    M. Steslicka, Prog. Surface Science,5, 178 (1974).

  10. 10.

    C. L. Roy and G. Roy, Physica,111B, 51 (1981).

  11. 11.

    L. F. Mattheiss and D. R. Hamann, Phys. Rev.,B29, 5372 (1984).

  12. 12.

    S. N. Molotkov and V. V. Tatarskii, Poverkhnost',5, 17 (1988).

  13. 13.

    O. Jepsen, Z. Madsen, and O. K. Anderson, Phys. Rev.,B18, 605 (1978).

  14. 14.

    H. Krakauer, M. Posternak, and A. J. Freeman, Phys. Rev.,B19, 1706 (1979).

  15. 15.

    W. Kohn and L. J. Sham, Phys. Rev. Rev.,A140, 1133 (1965).

  16. 16.

    L. Hedin and B. I. Lundqvist, Z. Phys.,C4, 2062 (1971).

  17. 17.

    E. V. Chulkov, V. M. Silkin, and E. N. Shirykalov, Fiz. Met. Metall.,64, 213 (1987).

  18. 18.

    L. Kleinman, Phys. Rev.,B21, 2630 (1980).

  19. 19.

    G. B. Bachelet and M. Schluter, Phys. Rev.,B25, 2103 (1982).

  20. 20.

    E. V. Chulkov, V. M. Silkin, A. G. Lipnitskii, and V. E. Panin, Electrochemica Acta,34, 19 (1989).

  21. 21.

    E. V. Chulkov, V. M. Silkin, and I. Y. Sklyadneva, Surface Science,231, 9 (1990).

  22. 22.

    K. Horn, B. Reihl, and A. Zartner, et al., Phys. Rev.B30, 1711 (1984).

  23. 23.

    E. V. Chulkov, V. M. Silkin, and E. N. Shirykalov, Surface Science,188, 287 (1987).

  24. 24.

    H. B. Michelson, J. Appl. Phys.,48, 4719 (1977).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 47–53, October, 1991.

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Lipnitskii, A.G., Nikiforov, A.V., Silkin, V.M. et al. Relativistic electronic structure of the Pb (001) surface. Soviet Physics Journal 34, 888–893 (1991). https://doi.org/10.1007/BF00898585

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Keywords

  • Band Structure
  • Surface State
  • Brillouin Zone
  • Surface Level
  • Electronic Band