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Cyclic hydrocarbons: nanoscopic (π)-SQUIDs?

  • M. Himmerich
  • P. G.J. van DongenEmail author
  • R. M. Noack
Solid and Condensed State Physics

Abstract.

A nonperturbative method for calculating persistent currents in molecules and nanoscopic quantum rings is presented. Starting from the extended Hubbard model on a ring threaded by an Aharonov-Bohm flux, a feedback term through which the current can generate magnetic flux is added. Another extension of the Hamiltonian describes the energy stored in the internally generated field. This model is evaluated using exact diagonalization and an iterative scheme to find the minima of the free energy with respect to the current. The magnetic properties due to electron delocalization of conjugated hydrocarbons like benzene [magnetic anisotropy, magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)] — that have become important criteria for aromaticity — can be examined using this model. A possible novel mechanism for a permanent orbital magnetic moment in quantum rings analogous to the one in π-SQUIDs is found in the framework of the proposed model. The quantum rings must satisfy two conditions to exhibit this kind of permanent orbital magnetic moment: a negative Drude weight and an inductivity above the critical level.

PACS.

31.15.Ct Semi-empirical and empirical calculations 33.15.Kr Electric and magnetic moments 75.75.+a Magnetic properties of nanostructures 

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References

  1. C.D. Dimitrakopoulos, D.J. Mascaro, IBM J. Res. & Dev. 45, 11 (2001) CrossRefGoogle Scholar
  2. Molecular Electronics: Science and Technology edited by A. Aviram, M.A. Ratner (New York Academy of Sciences, New York, 1998) Google Scholar
  3. M.D. Ventra, S.T. Pantelides, N.D. Lang, Phys. Rev. Lett. 88, 046801 (2002) CrossRefADSGoogle Scholar
  4. P. Lazzeretti, Progress in Nuclear Magnetic Resonance Spectroscopy 36, 1 (2000) CrossRefGoogle Scholar
  5. J.A.N.F. Gomes, R.B. Mallion, Chem. Rev. 101, 1349 (2001) CrossRefGoogle Scholar
  6. L. Pauling, J. Chem. Phys. 4, 673 (1936) CrossRefADSGoogle Scholar
  7. J.A. Pople, J. Chem. Phys. 24, 1111 (1956) MathSciNetCrossRefADSGoogle Scholar
  8. J.A. Elvidge, L.M. Jackman, J. Chem. Soc. 859 (1961) Google Scholar
  9. V.I. Minkin, M.N. Glukhovtsev, B.Y. Simkin, Aromaticity and Antiaromaticity: Electronic and Structural Aspects (John Wiley and Sons, 1994) Google Scholar
  10. W.H. Flygare, Chem. Rev. 74, 653 (1974) CrossRefGoogle Scholar
  11. H.J. Dauben, J.J.D. Wilson, J.L. Laity, J. Am. Chem. Soc. 90, 811 (1968) CrossRefGoogle Scholar
  12. H.J. Dauben, J.J.D. Wilson, J.L. Laity, J. Am. Chem. Soc. 91, 1991 (1969). CrossRefGoogle Scholar
  13. P. von Ragué Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R. van Eikema Hommes, J. Am. Chem. Soc. 118, 6317 (1996) CrossRefGoogle Scholar
  14. R.V. Williams, J.R. Armantrout, B. Twamley, R.H. Mitchell, T.R. Ward, S. Bandyopadhyay, J. Am. Chem. Soc. 124, 13495 (2002) CrossRefGoogle Scholar
  15. T. Helgaker, M. Jaszunski, K. Ruud, Chem. Rev. 99, 293 (1999) CrossRefGoogle Scholar
  16. M. Büttiker, Y. Imry, R. Landauer, Phys. Lett. 96A, 365 (1983) CrossRefGoogle Scholar
  17. F. London, J. Chem. Phys. 5, 837 (1937) CrossRefADSGoogle Scholar
  18. R.C. Haddon, J. Am. Chem. Soc. 101, 1722 (1979) CrossRefGoogle Scholar
  19. M. Sigrist, T.M. Rice, Rev. Mod. Phys 67, 503 (1995) CrossRefADSGoogle Scholar
  20. C.C. Tsuei, J.R. Kirtley, Rev. Mod. Phys. 72, 969 (2000) CrossRefADSGoogle Scholar
  21. E. Hückel, Z. Physik 70, (1931) Google Scholar
  22. C.A. Stafford, A.J. Millis, B.S. Shastry, Phys. Rev. B 43, 13660 (1991). CrossRefADSGoogle Scholar
  23. K. Ohno, Theor. Chim. Acta 2, 219 (1964) CrossRefGoogle Scholar
  24. C.W.M. Castleton, W. Barford, J. Chem. Phys. 117, 3570 (2002) CrossRefADSGoogle Scholar
  25. R.J. Bursill, C. Castleton, W. Barford, Chem. Phys. Lett. 294, 307 (1998) CrossRefADSGoogle Scholar
  26. R.M. Fye, M.J. Martins, D.J. Scalapino, J. Wagner, W. Hanke, Phys. Rev. B 44, 6909 (1991) CrossRefADSGoogle Scholar
  27. A.H. Silver, I.E. Zimmermann, Phys. Rev. 157, 317 (1967) CrossRefADSGoogle Scholar
  28. L.N. Bulaevskii, V.V. Kuzii, A.A. Sobyanin, JETP Lett. 25, 290 (1977) ADSGoogle Scholar
  29. D.J. Hartfield, Matrix theory and applications with MATLAB (CRC Press LLC, Boca Raton, 2001) Google Scholar
  30. B.P. Hillam, Math. Mag. 48, 167 (1975) zbMATHMathSciNetCrossRefGoogle Scholar
  31. H. Lueken, Magnetochemie (Teubner, Leipzig, 1999) Google Scholar
  32. J.A. Pople, J. Chem. Phys. 41, 2559 (1964) CrossRefADSGoogle Scholar
  33. A.F. Ferguson, J.A. Pople, J. Chem. Phys. 42, 1560 (1964) CrossRefADSGoogle Scholar
  34. B.P. Dailey, J. Chem. Phys. 41, 2304 (1964) CrossRefADSGoogle Scholar
  35. D. Loss, T. Martin, Phys. Rev. B 47, 4619 (1993) CrossRefADSGoogle Scholar
  36. D. Loss, Phys. Rev. Lett. 69, 343 (1992) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Institut für Physik, Johannes Gutenberg-Universität MainzGermany
  2. 2.Fachbereich Physik, Philipps-Universität MarburgMarburgGermany

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