Phonon softening, chaotic motion, and order-disorder transition in Sn/Ge(111)

Physical Review Letters

Volumn 91, Issue 1, 2003, Pages

  Faris D ^a   Kaminski W ^b,c   Lobo, J ^b,c   Ortega, J ^b   Hulpke, E ^d   Perez R ^b   Flores, F ^b   Michel, E G ^a  

^a INSTITUTO NICOLÁS CABRERA   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSITY OF WROC AW   (Poland)

^d MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BAND STRUCTURE; GERMANIUM; INTERFACES (MATERIALS); LOW TEMPERATURE EFFECTS; ORDER DISORDER TRANSITIONS; PHONONS; TIN;

CHAOTIC MOTION; LOW DIMENSIONAL MATERIALS; PHONON SOFTENING;

QUANTUM THEORY;

EID: 0043210636     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. B. N. J. Persson, Surf. Sci. Rep. 15, 1 (1992).
2. A. Mascaraque and E.G. Michel, J. Phys. Condens. Matter 14, 6005 (2002).
3. J. M. Carpinelli et al., Phys. Rev. Lett. 79, 2859 (1997).
4. J. Avila et al., Phys. Rev. Lett. 82, 442 (1999).
5. A. Mascaraque et al., Phys. Rev. Lett. 82, 2524 (1999).
6. J. Ortega et al., J. Phys. Condens. Matter 12, L21 (2000).
7. T. E. Kidd et al., Phys. Rev. Lett. 85, 3684 (2000).
8. R. I. G. Uhrberg and T. Balasubramanian, Phys. Rev. Lett. 81, 2108 (1998).
9. A. V. Melechko et al., Phys. Rev. B 61, 2235 (2000).
10. H. H. Weitering et al., Science 285, 2107 (1999).
11. G. Ballabio et al., Phys. Rev. B 61, R13345 (2000)
12. G. Ballabio et al., Phys. Rev. Lett. 89, 26803 (2002).
13. L. Floreano et al., Phys. Rev. B 64, 075405 (2001).
14. R. Pérez et al., Phys. Rev. Lett. 86, 4891 (2001).
15. L. Petersen et al., Phys. Rev. B 65, 020101(R) (2002).
16. H. J. Ernst, E. Hulpke, and J. P. Toennies, Phys. Rev. B 46, 16081 (1992).
17. D. Farías and K. H. Rieder, Rep. Prog. Phys. 61, 1575 (1998)
18. D. Farías et al., Phys. Rev. B 55, 7023 (1997).
19. -1 [18].
20. G. Benedek, in Helium Atom Scattering from Surfaces, edited by E. Hulpke (Springer-Verlag, Berlin, 1992), pp. 195-200.
21. Computer code CASTEP 4.2, academic version, licensed under the UKCP-MSI agreement, 1999. M. C. Payne et al., Rev. Mod. Phys. 64, 1045 (1992).
22. We use a (3 × 3) unit cell with three Sn atoms and six Ge layers, the last one being saturated with H atoms.
23. The fitting to the experiment and the PW calculation yield the same energetic order and character of the modes, with values at the Γ̄ point in reasonable agreement. The ground state energy of the (3 × 3) reconstruction with respect to the √3-ideal geometry, as calculated with the PW-GGA-DFT computer code, is ∼4 meV/Sn atom. This energy is probably too small to explain the observed transition temperature of ∼150 K. This suggests that the frequencies calculated above the only indicative and should be taken as a first approximation to the real spectrum at the Γ̄ point.
24. A. A. Demkov et al., Phys. Rev. B 52, 1618 (1995).
25. J. Ortega, R. Pérez, and F. Flores, J. Phys. Condens. Matter 14, 5979 (2002).
26. We use a (3 × 3) unit cell with four Ge layers and find that the (3 × 3) structure is lower than the ideal √3 reconstruction by ∼25 meV/Sn atom.
27. L. Petaccia et al., Phys. Rev. B 64, 193410 (2001).