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Simulations of Relaxation, Pinning, and Melting in Flux Lattices

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Phase Transitions and Relaxation in Systems with Competing Energy Scales

Part of the book series: NATO ASI Series ((ASIC,volume 415))

Abstract

Fundamental aspects of the physics of an elastic medium in a static random background potential are discussed by use of one – and two dimensional computer simulations. The role of non-linear elastic instabilities and plastic deformations are treated in detail. Elastic instabilities are needed for the existence of a pinning force. In the limit of infinite system size plastic deformations always occur.

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References

  1. L.D. Landau and E.M. Liftshits, Chap. 21 in Theory of Elasticity, Pergamon Press 1970.

    Google Scholar 

  2. H.J. Jensen, Y. Brechet, A. Brass, J. Low Temp. Phys. 74, 293 (1989).

    Article  ADS  Google Scholar 

  3. W. F. Vinen in Superconductivity,Vol. II, ed. R. D. Parks (Marcel Dekker, New York, 1969)

    Google Scholar 

  4. See also Y. B. Kim and M. J. Stephen, ibidem.

    Google Scholar 

  5. H. J. Jensen, A. Brass and A. J. Berlinsky, Phys. Rev. Lett. 60, 1676 (1988).

    Article  ADS  Google Scholar 

  6. A. Brass, H. J. Jensen, and A. J. Berlinsky, Phys. Rev. B 39, 102 (1989).

    Article  ADS  Google Scholar 

  7. E. H. Brandt, J. Low Temp. Phys. 53, 41, 71(1983)

    Article  ADS  Google Scholar 

  8. E. H. Brandt, Phys. Rev. Lett. 50, 1599 (1983).

    Article  ADS  Google Scholar 

  9. A. I. Larkin and Yu. N. Ovchinnikov in Nonegiuilibrium Superconductivity, ed. by D. N. Langenberg and A. I. Larkin (North Holland, 1986 ).

    Google Scholar 

  10. H.J. Jensen, Y. Brechet, and B. Doucot, J. Phys. I France 3, 611 (1993).

    Google Scholar 

  11. O. Pla and F. Nori, Phys. Rev. Lett. 67, 919 (1991).

    Article  ADS  Google Scholar 

  12. H. J. S. Feder and J. Feder, Phys. Rev. Lett. 66, 2669 (1991)

    Article  ADS  Google Scholar 

  13. H. J. S. Feder and J. Feder, Phys. Rev. Lett. 67, 283 (1991) (erratum).

    Article  ADS  Google Scholar 

  14. H.J. Jensen, Y. Brechet, B. Doucot, A. Brass, Submitted to Europhys. Lett.

    Google Scholar 

  15. C. Tang, K. Wiesenfeld, P. Bak, S. Coppersmith, and P. Littlewood, Phys. Rev. Lett. 58, 1161 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  16. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990)

    Article  ADS  Google Scholar 

  17. S.N. Coppersmith, ibid. 65, 1044 (1990)

    Article  ADS  Google Scholar 

  18. E.M. Chudnovsky, ibid. 65, 3060 (1990)

    Article  ADS  Google Scholar 

  19. J. Toner, ibid. 66, 2523 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  20. A. Houghton, R. A. Pelcovits, and A. Sudbo, J. P“vs.:Condensed Matter, 3, 7527 (1991).

    Article  ADS  Google Scholar 

  21. M.P.A. Fisher, T.A. Tohuyasu, Phys. Rev. Lett. 66, 2931 (1991)

    Article  ADS  Google Scholar 

  22. M.P.A. Fisher, Phys. Rev. Lett. 62, 1415 (1989)

    Article  ADS  Google Scholar 

  23. A. I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. 34, 409 (1979).

    Article  ADS  Google Scholar 

  24. J.P. McTague, D. Frenkel, and M.P. Allen, in Ordering in Two Dimensions, ed. S. K. Sinha, ( North Holland, 1980 ).

    Google Scholar 

  25. Y. Brechet, B. Doucot, H.J. Jensen, and A.-Ch. Shi, Phys. Rev. B 42, 2116 (1990).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. C.A. Murray, P.L. Gammel, D.J. Bishop, D.B. Mitzi, and A. Kapitulnik, Phys. Rev. Lett. 64, 2312 (1990)

    ADS  Google Scholar 

  28. D.G. Grier, C.A. Murray, C.A. Bolle, P.L. Gammel, D. J. Bishop, D.B. Mitzi, and A. Kapitulnik, ibid. 66, 2270 (1991).

    Article  ADS  Google Scholar 

  29. H.J. Jensen, A. Brass, Y. Brechet, and A.J. Berlinsky, Phys. Rev. B 38, 9235 (1988)

    Article  ADS  Google Scholar 

  30. This means that a rigid translation of the particle system requires a finite energy (see Ref. [16]) due to the fact that the random potential breaks the translational invariance.

    Google Scholar 

  31. E. Akkermans and R. Maynard, Phys. Rev. B 32, 7850 (1985)

    Article  ADS  Google Scholar 

  32. C.C. Yu and A. J. Leggett, Comments Condens. Matter Phys. 14, 231 (1988).

    Google Scholar 

  33. J.-P. Bouchaud, M. Mézard, and J.S. Yedidia, Phys. Rev. Lett. 67, 3840 (1991).

    Article  ADS  Google Scholar 

  34. It is interesting to note that recent high precision neutron scattering experiments on the flux line lattice in a clean Niobium sample by R.N. Kleiman, T.E. Mason and D.J. Bishop found that the best orientationally ordered flux line lattice was established by entering the superconducting state by slowly decreasing the magnetic field through Hc2 rather than field cooling or zero field cooling followed by an increase of the magnetic field. T.E. Mason, private communication.

    Google Scholar 

  35. H.J. Jensen, A. Brass, Y. Brechet, and A.J. Berlinsky, Cryogenics 29, 367 (1989).

    Article  Google Scholar 

  36. L.E. Rehn, P.R. Okamoto,J. Pearson, R. Bhadra, R. and M. Grimsditch, Phys. Rev. Lett. 59, 2987, (1987).

    Article  ADS  Google Scholar 

  37. To be consistent one has to expand the vortex-vortex energy to the same order in s as the random potential. However, it turns out that the anharmonic elasticity terms are irrelevant for the point we consider here, see Ref. [16]

    Google Scholar 

  38. R. Labusch, Cryst. Lattice Defects 1, 1 (1969).

    Google Scholar 

  39. J.P. Hirth and J. Lothe, Theory of Dislocations(McGraww-Hill, New York, 1968) p. 399

    Google Scholar 

  40. R. Hill, Proc. Phys. Soc. 65A, 349 (1952).

    ADS  Google Scholar 

  41. See Theory of Elasticity, L.D. Landau and E.M. Lifshitz (Pergamon Press, 1970) Sec. 21 for a discussion of elastic instabilities. This regime is “elastic” in the sense that the association of each particle with its neighbors in the flux lattice is unchanged by their motion through the random potential. By contrast, in the plastic regime, moving particles flow past neighbors which are pinned by the impurity potential.

    Google Scholar 

  42. M. Tinkam, Introduction to Superconductivity, (McGraw-Hill, New York, 1975) Chap. 5.

    Google Scholar 

  43. P. Thorel, R. Kahn, Y. Simon and D. Cribier, J. Physique, 34, 447 (1973).

    Article  Google Scholar 

  44. R.P. Huebener, Phys. Rep. C 13, 143 (1974).

    Article  ADS  Google Scholar 

  45. E.V. Thuneberg, J. Low Temp. Phys. 57, 415, (1984).

    Article  ADS  Google Scholar 

  46. E.H. Brandt, Phys. Rev. B 34, 6514, (1986).

    Article  ADS  Google Scholar 

  47. D.S. Fisher, Phys. Rev. Lett. 50, 1486 (1983).

    Article  ADS  Google Scholar 

  48. F. de la Cruz, J. Luzuriaga, E.N. Martinez, and E.J. Osquiguil, Phys. Rev. B 36, 6850 (1987).

    Article  ADS  Google Scholar 

  49. D.S. Fisher, in Nonlinearity in Condensed Matter, edited by Bishop, A. R., Campbell, D. K., Kumar, P. and Trullinger, S. E. ( Springer-Verlag, Berlin, 1987 ).

    Google Scholar 

  50. H.J. Jensen, A. Brass, A.-C. Shi, and A.J. Berlinsky, Phys. Rev. B 41, 6394 (1990).

    Article  ADS  Google Scholar 

  51. T. T. Palstra, B. Batlogg, L. F. Schneemeyer, and J..V. Waszczak, Phys. Rev. Lett. 61, 1662 (1988).

    Article  ADS  Google Scholar 

  52. M. Tinkham, Phys. Rev. Lett. 61, 1658 (1988).

    Article  ADS  Google Scholar 

  53. K. A. Müller, M. Takashige, and J. G. Bednorz, Phys. Rev. Lett. 58, 1143 (1987).

    Article  ADS  Google Scholar 

  54. Y. Yeshurun and A. P. Malozemoff, Phys. Rev. Lett. 60, 2202 (1988).

    Article  ADS  Google Scholar 

  55. P. H. Kes, J. Arts, J. van den Berg, C. J. van der Beek, and J. A. Mydosh, Supercond. Sci. Technol. 1, 242 (1989).

    Article  ADS  Google Scholar 

  56. C. Rossel, Y. Maeno, and I. Morgenstern, Phys. Rev. Lett. 62, 681 (1989).

    Article  ADS  Google Scholar 

  57. P. L. Gammel, L. F. Schneemeyer, J. V. Waszczak, and D. J. Bishop, Phys. Rev. Lett. 61, 1666 (1988) and 62, 2331 (1989).

    Article  ADS  Google Scholar 

  58. P. L. Gammel, L. F. Schneemeyer, J. V. Waszczak, and D. J. Bishop, Phys. Rev. Lett.62, 2331 (1989).

    Google Scholar 

  59. E. H. Brandt, P. Esquinazi, and G. Weiss, Phys. Rev. Lett. 62, 2330 (1989).

    Article  ADS  Google Scholar 

  60. D. S. Fisher, Phys. Rev. B 22, 1190 (1980)

    Article  ADS  Google Scholar 

  61. D. R. Nelson Phys. Rev. Lett. 60, 1973 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  62. D. R. Nelson and H. S. Seung, Phys. Rev. B39, 9153 (1989)

    Article  ADS  Google Scholar 

  63. R. S. Markiewicz, J. Phys. C Solid State Phys. 21, L1173 (1988)

    Article  ADS  Google Scholar 

  64. M. Moore, Phys. Rev. B. 39, 136 (1989)

    Article  ADS  Google Scholar 

  65. H. Houghton, R. A. Pelcovits, and A. Sudbø, Phys. Rev. B, in press

    Google Scholar 

  66. E. H. Brandt, Phys. Rev. Lett. 63, 1106 (1989)

    Article  ADS  Google Scholar 

  67. A. Brass and H. J. Jensen, Phys. Rev. B 39, 9587 (1989).

    Article  ADS  Google Scholar 

  68. F. Reif, Fundamentals of statistical and thermal physics, Chap. 15.11 (McGraw-Hill, 1965 ).

    Google Scholar 

  69. T. Schneider and E. Stoll, Phys. Rev B 17, 1302 (1978).

    Article  ADS  Google Scholar 

  70. E. H. Brandt, Phys. Stat. Sol. 77, 105 (1976).

    Article  ADS  Google Scholar 

  71. M. Tinkham, Introduction to Superconductivity, (McGraw-Hill, New York, 1975), Chap. 4.

    Google Scholar 

  72. This is the same system as the one used in Ref. [48]. The value for λ2 T c /d given in Ref. [48] contains a misprint. The correct value is λ2 T c /d = 10-2 cm.

    Google Scholar 

  73. The lattice constant of the triangular Abrikosov lattice is given by \({{a}_{0}} = {{(4/3)}^{{1/4}}}\sqrt {{2\pi /b}} \lambda /\kappa\)

    Google Scholar 

  74. It should be noted that since B c2 is temperature dependent the actual reduced field varies with temperature like b(t) = b(0)(1 + t 2 )/(1 - t 2. In the temperature range considered in Fig. 32 b(t) varies from 0.11 at t = 0.2 to 0.45 at t = 0.8.

    Google Scholar 

  75. J.P. Bouchaud, A. Comtet, A. Georges, and P. Le Doussal, J. Phys. France 48, 1445 (1987).

    Article  Google Scholar 

  76. W.J. Yeh and Y.H. Kao, Phys. Rev. Lett. 53,1590 (1984)

    Article  ADS  Google Scholar 

  77. W.J. Yeh and Y.H. Kao, Phys. Rev. B 44, 360 (1991).

    Article  ADS  Google Scholar 

  78. W.H. Press, Comments Astrophys. Space Phys. 7, 103 (1978).

    Google Scholar 

  79. P. Duta and P.M. Horn, Rev. Mod. Phys. 53, 497 (1981).

    Article  ADS  Google Scholar 

  80. M.B. Weissman, Rev. Mod. Phys. 60, 537 (1988).

    Article  ADS  Google Scholar 

  81. H.J. Jensen, Phys. Rev. Lett. 64, 3103 (1990).

    Article  ADS  Google Scholar 

  82. T. Fiig and H.J. Jensen, J. Stat. Phys., To be published.

    Google Scholar 

  83. J.V. Andersen, H.J. Jensen, and O.G. Mouritsen, Phys. Rev. B 44, 439 (1991).

    Article  ADS  Google Scholar 

  84. G. Grinstein, T. Hwa, and H.J. Jensen Phys. Rev A 45, R559 (1992).

    Article  ADS  Google Scholar 

  85. H.J. Jensen, Physica Scripta 39, 593 (1991).

    Article  ADS  Google Scholar 

  86. H.C. Fogedby, M.H. Jensen, Y.-C. Zhang, T. Bohr, H.J. Jensen, and H.H. Rugh, Mod. Phys. Rev. Lett. B 5, 1837 (1991).

    Article  MathSciNet  ADS  Google Scholar 

  87. S.H. Liu, Phys. Rev. B 16, 4218 (1977).

    Article  ADS  Google Scholar 

  88. P.M. Morse and H. Feshback Methods of Theoretical Physics, Chap 7. McGraw-Hill Book Company, New York (1953).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Imperial College, 180 Queen’s Gate, London, SW7 2BZ, UK

    Henrik Jeldtoft Jensen

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  1. Henrik Jeldtoft Jensen
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Editors and Affiliations

  1. Institutt for energiteknikk, POB 40, N-2007, Kjeller, Norway

    Tormod Riste (Director) (Director)

  2. Department of Physics, University of Oxford, UK

    David Sherrington (Co-director) (Co-director)

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Jensen, H.J. (1993). Simulations of Relaxation, Pinning, and Melting in Flux Lattices. In: Riste, T., Sherrington, D. (eds) Phase Transitions and Relaxation in Systems with Competing Energy Scales. NATO ASI Series, vol 415. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1908-5_8

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  • DOI: https://doi.org/10.1007/978-94-011-1908-5_8

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