Phason-induced dynamics of colloidal particles on quasicrystalline substrates

  • Justus A. Kromer
  • Michael Schmiedeberg
  • Johannes Roth
  • Holger Stark
Regular Article


Phasons are special hydrodynamic modes that occur in quasicrystals. The trajectories of particles due to a phasonic drift were recently studied by Kromer et al. (Phys. Rev. Lett. 108, 218301 (2012)) for the case where the particles stay in the minima of a quasicrystalline potential. Here, we study the mean motion of colloidal particles in quasicrystalline laser fields when a phasonic drift or displacement is applied and also consider the cases where the colloids cannot follow the potential minima. While the mean square displacement is similar to the one of particles in a random potential with randomly changing potential wells, there also is a net drift of the colloids that reverses its direction when the phasonic drift velocity is increased. Furthermore, we explore the dynamics of the structural changes in a laser-induced quasicrystal during the rearrangement process that is caused by a steady phasonic drift or an instantaneous phasonic displacement.

Graphical abstract


Soft Matter: Colloids and Nanoparticles 


  1. 1.
    D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)ADSCrossRefGoogle Scholar
  2. 2.
    D. Levine, P.J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984)ADSCrossRefGoogle Scholar
  3. 3.
    D. Levine, T.C. Lubensky, S. Ostlund, S. Ramaswamy, P.J. Steinhardt, J. Toner, Phys. Rev. Lett. 54, 1520 (1985)ADSCrossRefGoogle Scholar
  4. 4.
    C.L. Henley, M. de Boissieu, W. Steurer, Philos. Mag. 86, 1131 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    M. de Boissieu, Isr. J. Chem. 51, 1292 (2011)CrossRefGoogle Scholar
  6. 6.
    J.A. Kromer, M. Schmiedeberg, J. Roth, H. Stark, Phys. Rev. Lett. 108, 218301 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    M. Sandbrink, M. Schmiedeberg, Aperiodic Crystals, edited by S. Schmid, R.L. Withers, R. Lifshitz (Springer, Berlin, 2013)Google Scholar
  8. 8.
    H. Löwen, J. Phys.: Condens. Matter 13, R415 (2001)CrossRefGoogle Scholar
  9. 9.
    A. Ashkin, Phys. Rev. Lett. 24, 156 (1970)ADSCrossRefGoogle Scholar
  10. 10.
    A. Ashkin, Science 210, 1081 (1980)ADSCrossRefGoogle Scholar
  11. 11.
    M.M. Burns, J.M. Fournier, J.A. Golovchenko, Science 249, 749 (1990)ADSCrossRefGoogle Scholar
  12. 12.
    M. Schmiedeberg, J. Roth, H. Stark, Phys. Rev. Lett. 97, 158304 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    M. Schmiedeberg, H. Stark, Phys. Rev. Lett. 101, 218302 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    J. Mikhael, J. Roth, L. Helden, C. Bechinger, Nature 454, 501 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    M. Schmiedeberg, J. Mikhael, S. Rausch, J. Roth, L. Helden, C. Bechinger, H. Stark, Eur. Phys. J. E 32, 25 (2010)CrossRefGoogle Scholar
  16. 16.
    J. Mikhael, G. Gera, T. Bohlein, C. Bechinger, Soft Matter 7, 1352 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    M. Schmiedeberg, J. Roth, H. Stark, Eur. Phys. J. E 24, 367 (2007)CrossRefGoogle Scholar
  18. 18.
    C. Reichhardt, C.J. Olson Reichhardt, Phys. Rev. Lett. 106, 060603 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    T. Bohlein, C. Bechinger, Phys. Rev. Lett. 109, 058301 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    C. Reichhardt, C.J. Olson Reichhardt, J. Phys.: Condens Matter 25, 225702 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    J. Mikhael, M. Schmiedeberg, S. Rausch, J. Roth, H. Stark, C. Bechinger, Proc. Natl. Acad. Sci. 107, 7214 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    M. Schmiedeberg, H. Stark, J. Phys.: Condens. Matter 24, 284101 (2012)CrossRefGoogle Scholar
  23. 23.
    T. Bohlein, J. Mikhael, C. Bechinger, Nat. Mater. 11, 126 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    S.P. Gorkhali, J. Qi, G.P. Crawford, J. Opt. Soc. Am. B 23, 149 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    B.V. Derjaguin, L. Landau, Acta Physicochim. (USSR) 14, 633 (1941)Google Scholar
  26. 26.
    E.J. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948)Google Scholar
  27. 27.
    P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)ADSCrossRefGoogle Scholar
  28. 28.
    P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J.M. Rubi, A. Pérez-Madrid, Phys. Rev. E 65, 031104 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    C. Lutz, M. Reichert, H. Stark, C. Bechinger, Europhys. Lett. 74, 719 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    R.D.L. Hanes, C. Dalle-Ferrier, M. Schmiedeberg, M.C. Jenkins, S.U. Egelhaaf, Soft Matter 8, 2714 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    C. Emary, R. Gernert, S.H.L. Klapp, Phys. Rev. E 86, 061135 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    R. McGrath, J. Ledieu, E.J. Cox, R.D. Diehl, J. Phys.: Condens. Matter 14, R119 (2002)ADSCrossRefGoogle Scholar
  33. 33.
    M. Engel, M. Umezaki, H.-R. Trebin, T. Odagaki, Phys. Rev. E 82, 134206 (2010)CrossRefGoogle Scholar
  34. 34.
    L. Guidoni, B. Débret, A. di Stefano, P. Verkerk, Phys. Rev. A 60, R4233 (1999)ADSCrossRefGoogle Scholar
  35. 35.
    L. Sanchez-Palencia, L. Santos, Phys. Rev. A 72, 053607 (2005)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Justus A. Kromer
    • 1
  • Michael Schmiedeberg
    • 2
  • Johannes Roth
    • 3
  • Holger Stark
    • 4
  1. 1.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für Theoretische Physik 2: Weiche MaterieHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany
  3. 3.Institut für Theoretische und Angewandte PhysikUniversität StuttgartStuttgartGermany
  4. 4.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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