Nonquasiparticle structure in the photoemission spectra from the Be(0001) surface and determination of the electron self energy

S. LaShell; E. Jensen; T. Balasubramanian

doi:10.1103/PhysRevB.61.2371

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Nonquasiparticle structure in the photoemission spectra from the Be(0001) surface and determination of the electron self energy

S. LaShell and E. Jensen

T. Balasubramanian

Physics Department, Brandeis University, Waltham, Massachusetts 02454

MAX-Lab, Lund University, Lund S 22 1 00, Sweden

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Phys. Rev. B 61, 2371 – Published 15 January, 2000

DOI: https://doi.org/10.1103/PhysRevB.61.2371

Abstract

Complex structure in photoemission spectra of Be(0001) surface states near the Fermi energy is observed and explained as the effect of strong electron-phonon coupling. The weak momentum dependence of the electron-phonon contribution to the electron self energy Σ is exploited to determine Σ by direct inversion of the spectra.

References (17)

B. A. McDougall, T. Balasubramanian, and E. Jensen, Phys. Rev. B 51, 13 891 (1995).
T. Balasubramanian, E. Jensen, X. L. Wu, and S. L. Hulbert, Phys. Rev. B 57, R6866 (1998).
P. Hofmann, Y. Q. Cai, C. Grütter, and J. H. Bilgram, Phys. Rev. Lett. 81, 1670 (1998).
T. Valla, A. V. Fedorov, P. D. Johnson, and S. L. Hulbert, Phys. Rev. Lett. 83, 2085 (1999).
G. Borstel, Appl. Phys. A: Solids Surf. 38, 193 (1985).
S. Engelsberg and J. R. Schrieffer, Phys. Rev. 131, 993 (1963).
M. Hengsberger et al., Phys. Rev. Lett. 83, 592 (1999); M. Hengsberger, R. Frésard, D. Purdie, P. Segovia, and Y. Baer, Phys. Rev. B 60, 10 796 (1999).
R. Claessen et al., Phys. Rev. Lett. 69, 808 (1992); J. W. Allen, G.-H. Gweon, R. Claessen, and K. Matho, J. Phys. Chem. Solids 56, 1849 (1995); M. R. Norman, M. Randeria, H. Ding, and J. C. Campuzano, Phys. Rev. B 57, R11 093 (1998).
G. Grimvall, The Electron-Phonon Interaction in Metals (North-Holland, New York, 1981).
U. O. Karlsson et al., Solid State Commun. 49, 711 (1984); R. A. Bartynski, E. Jensen, T. Gustafsson, and E. W. Plummer, Phys. Rev. B 32, 1921 (1985).
P. T. Sprunger et al., Science 275, 1764 (1997).
E. V. Chulkov, V. M. Silkin, and E. N. Shirykalov, Surf. Sci. 188, 287 (1987); P. J. Feibelman and R. Stumpf, Phys. Rev. B 50, 17 480 (1994).
When the energy resolution is larger than kT and ω≃0 the effective analysis energy is pulled down from its nominal value by the strong energy dependence of the Fermi factor. In the determination of $Σ_{R},$ the peak position ${\tilde{ε}}_{k}$ is subtracted from the nominal analysis energy. Since the nominal energy is larger than the effective energy, the resulting $Σ_{R}$ is too large.
Because $ε_{k}$ and k are nearly proportional, there is no quantitative distinction between fitting in k space or in $ε_{k}$ space.
J. B. Hannon, E. J. Mele, and E. W. Plummer, Phys. Rev. B 52, 2090 (1996); J. B. Hannon (private communication).
E. D. Hansen, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 80, 1766 (1998).
Equation (2) can be trivially inverted, yielding $α^{2} F (ω) = (π ħ)^{- 1} \partial Σ_{I} (ω) / \partial ω,$ suggesting that ARP data with better statistics than these could be used to measure $α^{2} F (ω) .$

[c1] B. A. McDougall, T. Balasubramanian, and E. Jensen, Phys. Rev. B 51, 13 891 (1995).

[c2] T. Balasubramanian, E. Jensen, X. L. Wu, and S. L. Hulbert, Phys. Rev. B 57, R6866 (1998).

[c3] P. Hofmann, Y. Q. Cai, C. Grütter, and J. H. Bilgram, Phys. Rev. Lett. 81, 1670 (1998).

[c4] T. Valla, A. V. Fedorov, P. D. Johnson, and S. L. Hulbert, Phys. Rev. Lett. 83, 2085 (1999).

[c5] G. Borstel, Appl. Phys. A: Solids Surf. 38, 193 (1985).

[c6] S. Engelsberg and J. R. Schrieffer, Phys. Rev. 131, 993 (1963).

[c7] M. Hengsberger et al., Phys. Rev. Lett. 83, 592 (1999); M. Hengsberger, R. Frésard, D. Purdie, P. Segovia, and Y. Baer, Phys. Rev. B 60, 10 796 (1999).

[c8] R. Claessen et al., Phys. Rev. Lett. 69, 808 (1992); J. W. Allen, G.-H. Gweon, R. Claessen, and K. Matho, J. Phys. Chem. Solids 56, 1849 (1995); M. R. Norman, M. Randeria, H. Ding, and J. C. Campuzano, Phys. Rev. B 57, R11 093 (1998).

[c9] G. Grimvall, The Electron-Phonon Interaction in Metals (North-Holland, New York, 1981).

[c10] U. O. Karlsson et al., Solid State Commun. 49, 711 (1984); R. A. Bartynski, E. Jensen, T. Gustafsson, and E. W. Plummer, Phys. Rev. B 32, 1921 (1985).

[c11] P. T. Sprunger et al., Science 275, 1764 (1997).

[c12] E. V. Chulkov, V. M. Silkin, and E. N. Shirykalov, Surf. Sci. 188, 287 (1987); P. J. Feibelman and R. Stumpf, Phys. Rev. B 50, 17 480 (1994).

[c13] When the energy resolution is larger than kT and ω≃0 the effective analysis energy is pulled down from its nominal value by the strong energy dependence of the Fermi factor. In the determination of $Σ_{R},$ the peak position ${\tilde{ε}}_{k}$ is subtracted from the nominal analysis energy. Since the nominal energy is larger than the effective energy, the resulting $Σ_{R}$ is too large.

[c14] Because $ε_{k}$ and k are nearly proportional, there is no quantitative distinction between fitting in k space or in $ε_{k}$ space.

[c15] J. B. Hannon, E. J. Mele, and E. W. Plummer, Phys. Rev. B 52, 2090 (1996); J. B. Hannon (private communication).

[c16] E. D. Hansen, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 80, 1766 (1998).

[c17] Equation (2) can be trivially inverted, yielding $α^{2} F (ω) = (π ħ)^{- 1} \partial Σ_{I} (ω) / \partial ω,$ suggesting that ARP data with better statistics than these could be used to measure $α^{2} F (ω) .$

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Nonquasiparticle structure in the photoemission spectra from the Be(0001) surface and determination of the electron self energy

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References (17)

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