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Kouwenhoven, L.P.1
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(a) R.L. Whetten et al.: Adv. Mater. 5, 428 (1996); and in W. Andreoni (Ed.): Chemical Physics of Fullerenes 5 and 10 Years Later (Kluwer, Dordrecht 1996) pp. 475-490;
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Whetten, R.L.1
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(c) W.D. Luedtke, U. Landman: J. Phys. Chem. 100, 13 323 (1996); ibid: J. Phys. Chem. B 102, 6566 (1998);
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Chen, S.1
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33751386620
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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)]
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28
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0000487379
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0, are (a tilde indicates a local component): Au: ̃(2.50), p(3.00), d(2.00); S: s(1.80), p̃(2.30); C: s(1.50), p̃(1.54); H: s̃(0.95). The Au pseudopotential is relativistic and has been weighted averaged by the j degeneracy of the l ± 1/2 states [see L. Kleinman: Phys. Rev. B 21, 2630 (1980); G.B. Bachelet, M Schlüter: Phys. Rev. B 25, 2103 (1982)]
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0001483636
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0, are (a tilde indicates a local component): Au: ̃(2.50), p(3.00), d(2.00); S: s(1.80), p̃(2.30); C: s(1.50), p̃(1.54); H: s̃(0.95). The Au pseudopotential is relativistic and has been weighted averaged by the j degeneracy of the l ± 1/2 states [see L. Kleinman: Phys. Rev. B 21, 2630 (1980); G.B. Bachelet, M Schlüter: Phys. Rev. B 25, 2103 (1982)]
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Blick, R.H.1
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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)
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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, 14577 (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)]
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Yannouleas, C.1
Landman, U.2
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0001483578
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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, 14577 (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)]
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Comments At. Mol. Phys.
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Yannouleas, C.1
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52
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33751559766
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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, 14577 (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)]
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Z. Phys.
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Maruhn, J.1
Greiner, W.2
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53
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0001866320
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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, 14577 (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)]
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Wong, C.Y.1
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54
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0008998908
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note
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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
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55
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0009051778
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note
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b = 10 and 30 meV in Fig. 5).
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57
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0000976468
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Our sS-UHF employs N (mean-field) effective potentials and differs from the usual (restricted) HF in two ways: (i) it employs different orbitals for different spin directions (DODS), and (ii) it relaxes the requirement that the electron 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)] 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-symmetry 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, 39] 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 be obtained with LSD (e.g., pure spin density waves [29(c)]), spatial localization may require self-interaction corrections (SIC-LSD, see [40])
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(1993)
Phys. Rev. B
, vol.47
, pp. 2244
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Pfannkuche, D.1
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58
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0001366320
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Our sS-UHF employs N (mean-field) effective potentials and differs from the usual (restricted) HF in two ways: (i) it employs different orbitals for different spin directions (DODS), and (ii) it relaxes the requirement that the electron 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)] 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-symmetry 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, 39] 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 be obtained with LSD (e.g., pure spin density waves [29(c)]), spatial localization may require self-interaction corrections (SIC-LSD, see [40])
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Phys. Rev. B
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Fujito, M.1
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59
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0009001951
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[34], p. 1; For a general discussion of SB and the associated emergence of highly degenerate manifolds of excitations (Goldstone modes)
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(a) J. Paldus in [34], p. 1; For a general discussion of SB and the associated emergence of highly degenerate manifolds of excitations (Goldstone modes)
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Paldus, J.1
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61
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0003398525
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Springer, New York in the context of SB in finite systems and restoration of broken symmetries (Ch. 11)
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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);
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(1980)
The Nuclear Many-body Problem
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Ring, P.1
Schuck, P.2
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67
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85118959586
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note
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b = 0, 10 and 30 meV (see description in Fig. 5), as well as for a deformed single QD, did our LSD calculation yield (singlet) localized electron states
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68
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26144450583
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J.P. Perdew, A. Zunger: Phys. Rev. B 23, 5048 (1981); R.O. Jones, O. Gunnarsson: Rev. Mod. Phys. 61, 689 (1989)
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Phys. Rev. B
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Perdew, J.P.1
Zunger, A.2
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70
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0009033648
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note
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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
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