Skip to main content
SpringerLink
Log in
Book cover

Jamming, Yielding, and Irreversible Deformation in Condensed Matter pp 137–157Cite as

Depinning and Plasticity of Driven Disordered Lattices

  • Chapter

Part of the book series: Lecture Notes in Physics ((LNP,volume 688))

Abstract

We review in these notes the dynamics of extended condensed matter systems, such as vortex lattices in type-II superconductors and charge density waves in anisotropic metals, driven over quenched disorder. We focus in particular on the case of strong disorder, where topological defects are generated in the driven lattice. In this case the response is plastic and the depinning transition may become discontinuous and hysteretic.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. J. Liu and S. R. Nagel, Nature 391: 21 (1998); A. J. Liu, this proceedings.

    Article  ADS  Google Scholar 

  2. D. S. Fisher, Phys. Rep. 301: 113 (1998); and references therein.

    Article  ADS  Google Scholar 

  3. G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66: 1125 (1994).

    Article  ADS  Google Scholar 

  4. G. Grüner, Rev. Mod. Phys. 60: 1129 (1988).

    Article  ADS  Google Scholar 

  5. T. Giamarchi and S. Bhattacharya, in High Magnetic Fields: Applications to condensed matter physics and spectroscopy, C. Berthier. L. P. Lâevy, and G. Martinez, eds., p. 314 (Springer-Verlag, 2002).

    Google Scholar 

  6. E. Y. Andrei, Phys. Rev. Lett. 60: 2765 (1988).

    Article  ADS  Google Scholar 

  7. R. Seshadri and R. M. Westervelt, Phys. Rev. B 46: 5142 & 5150 (1992).

    Article  ADS  Google Scholar 

  8. D. S. Fisher, Phys. Rev. B 31, 1396 (1985).

    Article  ADS  Google Scholar 

  9. T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72: 1530 (1994); Phys. Rev. B 52: 1242 (1995).

    Article  ADS  Google Scholar 

  10. O. Narayan and D. S. Fisher, Phys. Rev. B 46: 11520 (1992).

    Article  ADS  Google Scholar 

  11. F. Nori, Science 271: 1373 (1996).

    Article  ADS  Google Scholar 

  12. A. Tonomura, Micron 30: 479 (1999).

    Article  Google Scholar 

  13. A. M. Troyanovski, J. Aarts and P. H. Kes, Nature 399: 665 (1999).

    Article  ADS  Google Scholar 

  14. A. Maeda, et al., Phys. Rev. B 65: 054506 (2002).

    Article  ADS  Google Scholar 

  15. P. B. Littlewood, Solid State Commun. 65: 1347 (1988).

    Article  ADS  Google Scholar 

  16. J. Levy, M. S. Sherwin, F. F. Abraham, and K. Wiesenfeld, Phys. Rev. Lett. 68: 2968 (1992).

    Article  ADS  Google Scholar 

  17. A. Montakhab, J. M. Carlson, and J. Levy, Phys. Rev. B 50: 11227 (1994).

    Article  ADS  Google Scholar 

  18. M. C. Marchetti, A. A. Middleton, and T. Prellberg, Phys. Rev. Lett. 85: 1104 (2000).

    Article  ADS  Google Scholar 

  19. J. M. Schwarz and D. S. Fisher, Phys. Rev. Lett. 87: 096107 (2001).

    Article  ADS  Google Scholar 

  20. M. C. Marchetti, A. A. Middleton, K. Saunders, and J. M. Schwarz, Phys. Rev. Lett. 91: 107002 (2003).

    Article  ADS  Google Scholar 

  21. S. H. Strogatz, C. M. Marcus, R. M. Westervelt, and R. E. Mirollo, Phys. Rev. Lett. 61: 2380 (1988); Physica D 36: 23 (1989).

    Article  ADS  Google Scholar 

  22. V. M. Vinokur and T. Nattermann, Phys. Rev. Lett. 79: 3471 (1997).

    Article  ADS  Google Scholar 

  23. K. Saunders, J. M. Schwarz, M. C. Marchetti, and A. A. Middleton, Phys. Rev. B 69: 37422 (2004).

    Google Scholar 

  24. M. C. Marchetti and K. A. Dahmen, Phys. Rev. B 66: 214201 (2002).

    Article  ADS  Google Scholar 

  25. J. M. Schwarz and D. S. Fisher, Phys. Rev. E 67: 21603 (2003).

    Article  ADS  Google Scholar 

  26. M. C. Marchetti, Pramana, 64: 1097 (2005).

    Article  ADS  Google Scholar 

  27. B. E. Rodriguez-Milla, M. C. Marchetti and A.A. Middleton, unpublished.

    Google Scholar 

  28. S. Zapperi, J. S. Andrade, Jr. and J. M. Filho, Phys. Rev. B 61, 14791 (2000).

    Article  ADS  Google Scholar 

  29. L. Balents. M. C. Marchetti and L. Radzihovsky, Phys. Rev. B 57: 7705 (1998).

    Article  ADS  Google Scholar 

  30. S. Scheidl, and V. M. Vinokur, Phys. Rev. E 57: 2574 (1998).

    Article  ADS  Google Scholar 

  31. T. Giamarchi and P. Le Doussal, Phys. Rev. B 57: 11356 (1998).

    Article  ADS  Google Scholar 

  32. Equation (11) should include a convective derivative that arises from the transformation to the laboratory frame [29]. This is negligible near a continuous depinning transition where the mean velocity is very small and it drops out in the mean field limit considered here. It will therefore be neglected, although it does play a crucial role on the dynamics well into the sliding state [29].

    Google Scholar 

  33. C. R, Myers and J. P. Sethna, Phys. Rev. B 47: 11171 (1993).

    Article  ADS  Google Scholar 

  34. A. A. Middleton, O. Biham, P. B. Littlewood, and P. Sibani: Phys. Rev. Lett. 68, 1586 (1992).

    Article  ADS  Google Scholar 

  35. A. A. Middleton, Phys. Rev. Lett. 68: 670 (1992).

    Article  ADS  Google Scholar 

  36. P. Le Doussal, K. J. Wiese, and P. Chauve, Phys. Rev. E 69: 26112 (2004).

    Article  Google Scholar 

  37. S. N. Coppersmith, Phys. Rev. Lett. 65: 1044 (1990); Phys. Rev. B 44: 2887 (1991).

    Article  ADS  Google Scholar 

  38. S. N. Coppersmith and A. J. Millis, Phys. Rev. B 44: 7799 (1991).

    Article  ADS  Google Scholar 

  39. A.-C. Shi and A. J. Berlinsky, Phys. Rev. Lett. 67: 1926 (1991).

    Article  ADS  Google Scholar 

  40. M. C. Faleski, M. C. Marchetti and A. A. Middleton, Phys. Rev. B 54: 12427 (1996).

    Article  ADS  Google Scholar 

  41. L. Balents, M. C. Marchetti, and L. Radzihovsky, Phys. Rev. Lett. 78: 751 (1997).

    Article  ADS  Google Scholar 

  42. A. Zippelius, B. I. Halperin, and D. R, Nelson, Phys. Rev. B 22: 2514 (1980).

    Article  ADS  Google Scholar 

  43. See, for instance, D. R. Nelson in Phase Transitions and Critical Phenomena, C. Domb and J. Lebowitz eds. (Academic, London, 1983), Vol. 7, pp. 76–79.

    Google Scholar 

  44. M. C. Marchetti and K. Saunders, Phys. Rev. B 66: 224113 (2002).

    Article  ADS  Google Scholar 

  45. J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980).

    Google Scholar 

  46. The strain-stress relation is nonlocal in both space and time. Only the nonlocality in time is retained here.

    Google Scholar 

  47. A. E. Koshelev and V. M. Vinokur, Phys. Rev. Lett. 73, 3580 (1994).

    Article  ADS  Google Scholar 

  48. K. Dahmen and J.P. Sethna, Phys. Rev. Lett. 71: 3222 (1993); Phys. Rev. B 53: 14872 (1996).

    Article  ADS  Google Scholar 

  49. R. da Silveira and M. Kardar, Phys. Rev. E 59: 1355 (1999).

    Article  ADS  Google Scholar 

  50. C. J. Olson, C. Reichhardt and V. M. Vinokur, Phys. Rev. B 64: 140502 (2001).

    ADS  Google Scholar 

  51. R, Maimon and J. M. Schwarz, Phys. Rev. Lett. 92: 255502 (2004).

    Article  ADS  Google Scholar 

  52. C. J. Olson, C. Reichhardt, and F. Nori, Phys. Rev. Lett. 81: 3757 (1998).

    Article  ADS  Google Scholar 

  53. N. Gronbech-Jensen, A. R. Bishop, and D. Dominguez, Phys. Rev. Lett. 76: 2985 (1996).

    Article  ADS  Google Scholar 

  54. S. Bhattacharya and M. J. Higgins, Phys. Rev. Lett. 70: 2617 (1993); M. J. Higgins and S. Bhattacharya, Physica C 257: 232 (1996).

    Article  ADS  Google Scholar 

  55. Y. Paltiel, E. Zeldov, Y. N. Myasoedov, K. Shtrikman, S. Bhattacharya, M. J. Higgins, Z. L. Xiao, E. Andrei, P. L. Gammel, and D. J. Bishop, Nature 403: 398 (2000).

    Article  ADS  Google Scholar 

  56. Y. Paltiel, Y. Myasoedov, E. Zeldov, G. Jung, M.L. Rappaport, D. E. Feldman, M.J. Higgins, and S. Bhattacharya, Phys. Rev. B 66: 60503 (2002).

    Article  ADS  Google Scholar 

  57. M. Marchevsky, M. J. Higgins, and S. Bhattacharya, Phys. Rev. Lett. 88: 87002 (2002).

    Article  ADS  Google Scholar 

  58. M. J. Higgins, A. A. Middleton, and S. Bhattacharya Phys. Rev. Lett. 70: 3784–3787 (1993).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Syracuse University, Syracuse, NY, 13244, USA

    M.C. Marchetti

Authors
  1. M.C. Marchetti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departament de Física Fonamental, Facultat de Física, Diagonal 647, Barcelona, 08028, Spain

    M. Carmen Miguel  & Miguel Rubi  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

Marchetti, M. (2006). Depinning and Plasticity of Driven Disordered Lattices. In: Miguel, M.C., Rubi, M. (eds) Jamming, Yielding, and Irreversible Deformation in Condensed Matter. Lecture Notes in Physics, vol 688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33204-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation