Skip to main content

Structures and spectra of gold nanoclusters and quantum dot molecules

  • Conference paper
Book cover The European Physical Journal D

Abstract

Size-evolutions of structural and spectral properties in two types of finite systems are discussed. First we focus on energetics and structures of gold clusters, particularly Au N in the 40 ≲ N ≲ 200 range exhibiting a discrete sequence of optimal clusters with a decahedral structural motif, and on the electronic structure of bare and methyl-thiol passivated Au38 clusters. Subsequently, bonding and spectra of quanturn dot molecules (QDM’s) are investigated, using a single-particle two-center oscillator model and the local-spin-density (LSD) method, for a broad range of interdot distances and coupling strengths. A molecular orbital classification of the QDM states correlates between the united-dot and separated-dots limits. LSD addition energies and spin polarization patterns for QDM’s in the entire coupling range are analyzed, guiding the construction of a constant interaction model. A generalization of the non-interacting-electrons Darwin—Fock model to QDM’s is presented. Wigner crystallization of the electrons leading to formation of Wigner supermolecules is explored in both the field-free case and with a magnetic field using a spin-andspace unrestricted Hartree—Fock Method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Haberland (Ed.): Clusters of Atoms and Molecules, Springer Series in Chemical Physics 52 and 57 (Springer, 27. Berlin 1994 )

    Google Scholar 

  2. W.A. deHeer: Rev. Mod. Phys. 65, 611 (1993)

    Article  ADS  Google Scholar 

  3. see C. Yannouleas, U. Landman: in Large Clusters of Atomsand Molecules, ed. by T.P. Martin ( Kluwer, Dordrecht 28. 1996 ) p. 131

    Google Scholar 

  4. T.P. Martin: Phys. Rep. 273, 199 (1996) 29.

    Google Scholar 

  5. L.P. Kouwenhoven et al.: in Mesoscopic Eletron Transport ed. by L.L. Sohn et al. (Kluwer, Dordrecht 1997) p. 105

    Google Scholar 

  6. R. Ashoori: Nature 379, 413 (1996)

    Article  ADS  Google Scholar 

  7. S. Tarucha: Phys. Rev. Lett. 77, 3613 (1996)

    Article  ADS  Google Scholar 

  8. U. Landman, W.D. Luedtke, N.A. Burnham, R. J. Colton: 30. Science 248, 454 (1990) 31.

    Google Scholar 

  9. See articles in P. Serena, N. Garcia (Eds.): Nanourires, ( Kluwer, Dordrecht 1997 )

    Google Scholar 

  10. R.N. Barnett, U. Landman: Nature 387, 788 (1997)

    Article  ADS  Google Scholar 

  11. C. Yannouleas, U. Landman: J. Phys. Chem. B 101, 5780 (1997); C. Yannouleas, E.N. Bogachek, U. Landman: Phys. Rev. B 57, 4872 (1998)

    Google Scholar 

  12. a) R.L. Whetten et al.: Adv. Mater. 5, 428 (1996); and in W. Andreoni (Ed.): Chemical Physics of Fulle.renes 5and 10 Years Later (Kluwer, Dordrecht 1996) pp. 475–33. 490; (b) C.L. Cleveland et al.: Z. Phys, D 40, 503 (1997); (c) W.D. Luedtke, U. Landman: J. Phys. Chem, 100, 13 323 (1996); ibid: J. Phys. Chem, B 102, 6566 (1998); (d) C.L. Cleveland et al.: Phys. Rev. Lett. 79, 1873 (1997)

    Google Scholar 

  13. S. Chen et al.: Science 280, 2098 (1998), and references to earlier work therein

    Google Scholar 

  14. a) M.M. Alvarez et al.: Chem. Phys, Lett. 266, 91 (1997); (h) T.G. Schaaff J. Phys. Chem. B 101, 7885 (1997)

    Google Scholar 

  15. C.L. Cleveland, U. Landman: J. Chem. Phys. 94, 7376 34. (1991)

    Google Scholar 

  16. L.D. Marks: Philos. Mag. 49, 81 (1984)

    Article  ADS  Google Scholar 

  17. For a recent review, see D.M.P. Mingos:. J. Chem. Soc. Dal- 35. ton 5, 561 (1996)

    Google Scholar 

  18. Our analysis, based on atomistic energy minimization, is essentially parameter-free and should be contrasted with multi-parameter data-fitting procedures using guessed structures including weighted distributions of cluster sizes with differing structural and morphological motifs [see e.g., W. Vogel, B. Rosner, B. Tesche: J. Phys. Chem. 97, 11 611 (1993)]

    Google Scholar 

  19. N. Ti-oullier, J.L. Martins: Phys. Rev. B 43. 1993 (1991)

    Google Scholar 

  20. The core radii, in ao, are (a tilde indicates a local component): Au: 5(2.50), p(3,00), d(2.00); s(1.80),f)(2.30); C: s(1.50), i(1.54); H: 5(0.95). The Au pseudopotential is relativistic and has been weighted averaged by the j degeneracy of the 1± 1/2 states [see L. Kleinman: Phys, Rev. B 21, 2630 (1980); G.B. Bachelet, I Schluter: Phys. Rev. B 25, 2103 (1982)]

    Google Scholar 

  21. R.N. Barnett, U. Landman: Phys. Rev. B 48, 2081 (1993)

    Article  ADS  Google Scholar 

  22. D.A. Papaconsta.ntopoulos: Handbook of the hand structure Of elemental solids ( Plenum, New York 1986 )

    Google Scholar 

  23. J.T. Khoury, R.L. Whetten: private communication

    Google Scholar 

  24. H. Häkkinen, R.N. Barnett, U. Landman: Phys. Rev. Lett. 82, 3264 (1999)

    Article  ADS  Google Scholar 

  25. L.P. Kouwenhoven: Science 268, 1440 (1995); F.R. Waugh et al.: Phys. Rev. Lett. 75, 705 (1995); N.C. van der Waart et al.: Phys. Rev. Lett. 74, 4702 (1995); R.H. Blick et al.: Phys. Rev. Lett. 80, 4032 (1998) and Phys. Rev. B 53, 7899 (1996)

    Google Scholar 

  26. V. Fock: Z. Phys. 47, 446 (1928); C.C. Darwin: Proc. Cambridge Philos. Soc, 27, 86 (1930)

    Google Scholar 

  27. a) D. Pfannkuche, V. Gudmundsson, P.A. Maksym: Phys. Rev. B 47, 2244 (1993); (b) J.J. Palacios et al.: Phys. Rev. B 50, 5760 (1994); (c) M. Fujito, A. Natori, H. Yasunaga: Phys. Rev, B 53, 9952 (1996)

    Google Scholar 

  28. C. Yannouleas, U. Landrnan: Phys. Rev. Lett. 82, 5325 (1999)

    Article  ADS  Google Scholar 

  29. a) M. Macucci et al.: Phys. Rev, B 55, R4879 (1997); (b) 1.-H. Lee et al.: ibid. 57. 9035 (1998); (c) M. Koskinen, M. Manninen, S.M. Rein-iann: Phys. Rev. Lett. 79, 1389 (1997); (d) M. Ferconi, G. Vignale: Phys. Rev. B 50, 14 722 (1994)

    Google Scholar 

  30. M. Eto: Jpn. App!. Phys. 36, 3924 (1997)

    Article  Google Scholar 

  31. A 3D field-free version of the TCOM has been used in the description of fission in metal clusters [C. Yannouleas, U. Landman: J. Phys. Chem. 99, 14 577 (1995); C. Yannouleas et al.: Comments At. Mol. Phys. 31, 445 (1995)] and nuclei [J. Maruhn, W. Greiner: Z. Phys. 251, 431 (1972); C.Y. Wong: Phys. Lett. 30B, 61 (1969)]

    Google Scholar 

  32. The method described in [21] was used with a 60.16 Ry* [Ry*(GaAs) = 5.48 meV] kinetic-energy cutoff for the plane wave basis

    Google Scholar 

  33. For a single 2D isotropic harmonic oscillator, peaks in AE spectra at shell closures (N = 2, 6, 12, 20,…) and half-shell closures (IV -= 4, 9, 16,…) are expected (see e.g. the QD curve in Fig. 5, although Veff exhibits deviations from harmonicity). For QDM’s with a. sufficiently large barrier between the dots, such shell-closure effects occur at twice the single QD electron numbers, for states lying below the barrier (see e.g. N = 4 for QDM’s with 1,’“hbai]e = 10 and 30 meV in Fig. 5)

    Google Scholar 

  34. Y.G. Smeyers: in R. Carb6, M. Klobukowski (Eds.): Self-Consistent Field: Theory and Applications ( Elsevier, Amsterdarn 1990 ) p. 80

    Google Scholar 

  35. Our sS-UHF employs N (mean-field) effective potentials and differs from the usual (restricted) BF in two ways: (i) it employs different orbitals for different spin directions (DODS), and (ii) it relaxes the requirement that the elec104 The European Physical Journal D trop wave functions be constrained by the symmetry of the external confining field. Earlier HF studies of single QD’s did not incorporate the spin-and-Space unrestrictions simultaneously. For example; Wigner molecules (at B = 0 and/or finite B) were not found by D. Pfannkuche et al.: [Phys. Rev. B 47, 2244 (1993)1 and M. Fujito et al.: [Phys. Rev, B 53, 9952 (1996)]. Indeed, using symmetry-restricted variational Wave functions, we have reproduced the results of these studies, while with the sS-UHF, with no such restrictions, broken-synunetry solutions with lower energy were obtained as described here. We further note here that employing a Space-UHF, but only for fully polarized single QD’s (i.e., under high magnetic fields where the spin unrestriction is not at play). Wigner crystallization has been investigated [38(b)]. LSD calculations [29, 391 where there are only two effective potentials (associated with the two spin directions) cannot yield in general crystallized solutions (except for N = 2 in a deformed single QD and in a QDM [39]). While certain symmetry breaking can he obtained with LSD (e.g., pure spin density waves [29(c)]), spatial localization may require self-interaction corrections (SIC-LSD, see [40])

    Google Scholar 

  36. a) J. Palcitis in [341, p. 1; For a general discussion of SB and the associated emergence of highly degenerate manifolds of excitations (Goldstone modes) see: (b) P.W. Anderson, Basic Notions of Condensed Matter.Physies (Benjamin, Menlo Park, CA 1984), and (c) P. Ring, P. Schuck: The Nuclear Many-Body Problem (Springer, New York 1980), in the context of SB in finite systems and restoration of broken symmetries (Ch. 11); (d) D.J. Thouless: Nucl. Phys. 21, 225 (1960)

    Google Scholar 

  37. E. Wigner: Phys. Rev. 46, 1002 (1934)

    Article  ADS  Google Scholar 

  38. a) P.A. Maksym: Physica B 184, 385 (1993); (b) H.-M. S.E. Koonin: Phys. Rev. B 54, 14 532 (1996); (c) V. Häusler: Z. Phys. B 99. 551 (1996)

    Google Scholar 

  39. We remark that only in the case of N = 2 and for the Q.D1\d’s with 17.01’-=. 0, 10 and 30 ma’. (see description in Fig. 5), as well as for a deformed single QD, did our LSD calculation yield (singlet) localized electron states

    Google Scholar 

  40. J.P. Perdew, A. Zunger: Phys. Rev, B 23.5048 (1981); R.O. Jones, O. Gunnarssom Rev. Mod. Phys. 61, 689 (1989)

    Article  Google Scholar 

  41. This includes spectroscopical probing of the intrinsic electronic spectra of the SB states, and of the rotational and vibrational spectra (Goldstone modes [36(b and c)]) of the symmetry broken states (WM’s) using radio and/or microwave frequencies (and possibly employing polarized radiation), as well as studies of the effect of impurities on the formation of SB states and their spectra; for investigations of impurity-pinning effects, see C. Yannouleas, U. Landman, to be published

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Italia

About this paper

Cite this paper

Barnett, R.N., Cleveland, C.L., Häkkinen, H., Luedtke, W.D., Yannouleas, C., Landman, U. (1999). Structures and spectra of gold nanoclusters and quantum dot molecules. In: Châtelain, A., Bonard, JM. (eds) The European Physical Journal D. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88188-6_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-88188-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88190-9

  • Online ISBN: 978-3-642-88188-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics