Advertisement

Journal of Experimental and Theoretical Physics

, Volume 126, Issue 2, pp 224–236 | Cite as

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

  • A. V. Samokhvalov
  • A. S. Melnikov
Order, Disorder, and Phase Transition in Condensed System
  • 19 Downloads

Abstract

We have proposed and developed a microscopic model of depinning (escape) of a multiquantum vortex in a superconductor with a cylindrical nonconducting cavity with the transverse size smaller than or on the order of the superconducting coherence length ξ0 at zero temperature. The spectrum of subgap quasiparticle excitations in two- and three-quantum vortices trapped by a cylindrical cavity has been calculated in the quasiclassical approximation. It is shown that the transformation of the spectrum is accompanied by break of anomalous spectral branches due to normal reflection of quasiparticles from the surface of a defect. A microscopic (spectral) criterion for multiquantum vortex pinning has been proposed; according to this criterion, the multiquantum vortex can be trapped in the cavity during the formation of a minigap in the elementary excitation spectrum near the Fermi level. Self-consistent calculations of density of states N(r, ε) for two- and three-quantum vortices trapped by a cylindrical cavity of radius on the order of ξ0 have been performed using quasiclassical Eilenberger equations. In the pure limit and for low temperatures TT c , peculiarities observed in the N(r, ε) distribution reflect the presence of M anomalous spectral branches in the M-quantum vortex and confirm the correctness of the spectral criterion of pinning (depinning) of a multiquantum vortex.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Campbell and J. E. Evetts, Critical Currents in Superconductors (Taylor and Francis, London, 1972).Google Scholar
  2. 2.
    G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    P. Yang and Ch. M. Lieber, Science 273, 1836 (1996).ADSCrossRefGoogle Scholar
  4. 4.
    M. Peurla, H. Huhtinen, M. A. Shakhov, K. Traito, Yu. P. Stepanov, M. Safonchik, P. Paturi, Y. Y. Tse, R. Palai, and R. Laiho, Phys. Rev. B 75, 184524 (2007).ADSCrossRefGoogle Scholar
  5. 5.
    A. F. Hebard, A. T. Fiory, and S. Somekh, IEEE Trans. Magn. 1, 589 (1977).ADSCrossRefGoogle Scholar
  6. 6.
    A. N. Lykov, Solid State Commun. 86, 531 (1993).ADSCrossRefGoogle Scholar
  7. 7.
    M. Baert, V. V. Metlushko, R. Jonckheere, V. V. Moshchalkov, and Y. Bruynseraede, Phys. Rev. Lett. 74, 3269 (1995).ADSCrossRefGoogle Scholar
  8. 8.
    L. Civale, A. D. Marwick, M. W. McElfresh, T. K. Worthington, A. P. Malozemoff, F. H. Holtzberg, J. R. Thompson, and M. A. Kirk, Phys. Rev. Lett. 65, 1164 (1990).ADSCrossRefGoogle Scholar
  9. 9.
    L. Civale, A. D. Marwick, T. K. Worthington, M. A. Kirk, J. R. Thompson, L. Krusin-Elbaum, Y. Sun, J. R. Clem, and F. H. Holtzberg, Phys. Rev. Lett. 67, 648 (1991).ADSCrossRefGoogle Scholar
  10. 10.
    C. P. Bean and J. D. Livingston, Phys. Rev. Lett. 12, 14 (1971).ADSCrossRefGoogle Scholar
  11. 11.
    G. S. Mkrtchyan and V. V. Shmidt, Sov. Phys. JETP 34, 195 (1971).ADSGoogle Scholar
  12. 12.
    M. Tinkham, Introduction to Superconductivity (Dover, New York, 2004; Atomizdat, Moscow, 1980).Google Scholar
  13. 13.
    H. Nordborg and V. M. Vinokur, Phys. Rev. B 62, 12408 (2000).ADSCrossRefGoogle Scholar
  14. 14.
    A. Buzdin and D. Feinberg, Phys. C (Amsterdam, Neth.) 256, 303 (1996).ADSCrossRefGoogle Scholar
  15. 15.
    A. Buzdin and M. Daumens, Phys. C (Amsterdam, Neth.) 294, 257 (1998).ADSCrossRefGoogle Scholar
  16. 16.
    A. Buzdin and M. Daumens, Phys. C (Amsterdam, Neth.) 332, 108 (2000).ADSCrossRefGoogle Scholar
  17. 17.
    A. A. Bespalov and A. S. Melnikov, Supercond. Sci. Technol. 26, 085014 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    S. M. Maurer, N.-C. Yeh, and T. A. Tombrello, Phys. Rev. B 54, 15372 (1996).ADSCrossRefGoogle Scholar
  19. 19.
    S. M. Maurer, N.-C. Yeh, and T. A. Tombrello, J. Phys.: Condens. Matter 10, 7429 (1998).ADSGoogle Scholar
  20. 20.
    D. J. Priour, Jr. and H. A. Fertig, Phys. Rev. B 67, 054504 (2003).ADSCrossRefGoogle Scholar
  21. 21.
    B. Rosenstein, I. Shapiro, and B. Ya. Shapiro, Phys. Rev. B 81, 064507 (2010).ADSCrossRefGoogle Scholar
  22. 22.
    N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Clarendon, Oxford, 2001).CrossRefGoogle Scholar
  23. 23.
    C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964).ADSCrossRefGoogle Scholar
  24. 24.
    F. Guinea and Yu. Pogorelov, Phys. Rev. Lett. 74, 462 (1995).ADSCrossRefGoogle Scholar
  25. 25.
    M. V. Feigel’man and M. A. Skvortsov, Phys. Rev. Lett. 78, 2640 (1997).ADSCrossRefGoogle Scholar
  26. 26.
    M. A. Skvortsov, D. A. Ivanov, and G. Blatter, Phys. Rev. B 67, 014521 (2003).ADSCrossRefGoogle Scholar
  27. 27.
    A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998).ADSCrossRefGoogle Scholar
  28. 28.
    A. A. Koulakov and A. I. Larkin, Phys. Rev. B 59, 12021 (1999).ADSCrossRefGoogle Scholar
  29. 29.
    N. B. Kopnin, Phys. Rev. B 60, 581 (1999).ADSCrossRefGoogle Scholar
  30. 30.
    E. V. Thuneberg, J. Kurkijarvi, and D. Rainer, Phys. Rev. Lett. 48, 1853 (1982).ADSCrossRefGoogle Scholar
  31. 31.
    E. V. Thuneberg, J. Kurkijarvi, and D. Rainer, Phys. Rev. B 29, 3913 (1984).ADSCrossRefGoogle Scholar
  32. 32.
    A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 28, 1200 (1968).ADSGoogle Scholar
  33. 33.
    G. Eilenberger, Z. Phys. 214, 195 (1968).ADSCrossRefGoogle Scholar
  34. 34.
    E. V. Thuneberg, J. Low Temp. Phys. 57, 415 (1984).ADSCrossRefGoogle Scholar
  35. 35.
    E. V. Thuneberg, J. Low Temp. Phys. 62, 27 (1986).ADSCrossRefGoogle Scholar
  36. 36.
    M. Friesen and P. Muzikar, Phys. Rev. B 53, R11953 (1986).ADSCrossRefGoogle Scholar
  37. 37.
    A. S. Mel’nikov, A. V. Samokhvalov, and M. N. Zubarev, Phys. Rev. B 79, 134529 (2009).ADSCrossRefGoogle Scholar
  38. 38.
    B. Rosenstein, I. Shapiro, E. Deutch, and B. Ya. Shapiro, Phys. Rev. B 84, 134521 (2011).ADSCrossRefGoogle Scholar
  39. 39.
    N. N. Bogolyubov, Sov. Phys. JETP 7, 41 (1958).Google Scholar
  40. 40.
    P. G. de Gennes, Superconductivity of Metals and Alloys (Bengamin, New York, 1966; Mir, Moscow, 1968).zbMATHGoogle Scholar
  41. 41.
    A. S. Mel’nikov, A. V. Samokhvalov, and V. L. Vadimov, JETP Lett. 102, 775 (2015).ADSCrossRefGoogle Scholar
  42. 42.
    V. L. Vadimov and A. S. Mel’nikov, J. Low Temp. Phys. 183, 342 (2016).ADSCrossRefGoogle Scholar
  43. 43.
    E. M. Lifshits and L. P. Pitaevski, Course of Theoretical Physics, Vol. 9: Statistical Physics, Part 2 (Nauka, Moscow, 1978; Pergamon, New York, 1980).Google Scholar
  44. 44.
    A. S. Mel’nikov and A. V. Samokhvalov, JETP Lett. 94, 759 (2011).CrossRefGoogle Scholar
  45. 45.
    P. A. Ioselevich and M. V. Feigel’man, Phys. Rev. Lett. 106, 077003 (2011).ADSCrossRefGoogle Scholar
  46. 46.
    P. A. Ioselevich, P. M. Ostrovsky, and M. V. Feigel’man, Phys. Rev. B 86, 035441 (2012).ADSCrossRefGoogle Scholar
  47. 47.
    A. L. Rakhmanov, A. V. Rozhkov, and F. Nori, Phys. Rev. B 84, 075141 (2011).ADSCrossRefGoogle Scholar
  48. 48.
    R. S. Akzyanov, A. V. Rozhkov, A. L. Rakhmanov, and F. Nori, Phys. Rev. B 89, 085409 (2014).ADSCrossRefGoogle Scholar
  49. 49.
    G. Karapetrov, J. Fedor, M. Iavarone, D. Rosenmann, and W. K. Kwok, Phys. Rev. Lett. 95, 167002 (2005).ADSCrossRefGoogle Scholar
  50. 50.
    I. V. Grigorieva, W. Escoffier, V. R. Misko, B. J. Baelus, F. M. Peeters, L. Y. Vinnikov, and S. V. Dubonos, Phys. Rev. Lett. 99, 147003 (2007).ADSCrossRefGoogle Scholar
  51. 51.
    A. V. Silhanek, S. Raedts, M. J. Van Bael, and V. V. Moshchalkov, Phys. Rev. B 70, 054515 (2004).ADSCrossRefGoogle Scholar
  52. 52.
    A. I. Buzdin, Phys. Rev. B 47, 11416 (1993).ADSCrossRefGoogle Scholar
  53. 53.
    V. A. Schweigert, F. M. Peeters, and P. S. Deo, Phys. Rev. Lett. 81, 2783 (1998).ADSCrossRefGoogle Scholar
  54. 54.
    A. S. Mel’nikov, I. M. Nefedov, D. A Ryzhov, I. A. Shereshevskii, V. M. Vinokur, and P. P. Vysheslavtsev, Phys. Rev. B 65, 140503 (2002).ADSCrossRefGoogle Scholar
  55. 55.
    A. Bezryadin, A. Buzdin, and B. Pannetier, Phys. Lett. A 195, 373 (1994).ADSCrossRefGoogle Scholar
  56. 56.
    G. E. Volovik, JETP Lett. 57, 244 (1993).ADSGoogle Scholar
  57. 57.
    Y. Tanaka, S. Kashiwaya, and H. Takayanagi, Jpn. J. Appl. Phys. 34, 4566 (1995).ADSCrossRefGoogle Scholar
  58. 58.
    D. Rainer, J. A. Sauls, and D. Waxman, Phys. Rev. B 54, 10094 (1993).ADSCrossRefGoogle Scholar
  59. 59.
    A. S. Mel’nikov and V. M. Vinokur, Nature 415, 60 (2002).ADSCrossRefGoogle Scholar
  60. 60.
    A. S. Mel’nikov and V. M. Vinokur, Phys. Rev. B 65, 224514 (2002).ADSCrossRefGoogle Scholar
  61. 61.
    A. S. Mel’nikov, D. A. Ryzhov, and M. A. Silaev, Phys. Rev. B 78, 064513 (2008).ADSCrossRefGoogle Scholar
  62. 62.
    S. M. M. Virtanen and M. M. Salomaa, Phys. Rev. B 60, 145581 (1999).CrossRefGoogle Scholar
  63. 63.
    M. A. Silaev and V. A. Silaeva, J. Phys.: Condens. Matter 25, 225702 (2013).ADSGoogle Scholar
  64. 64.
    M. Eschrig, D. Rainer, and J. A. Sauls, Vortices in Unconventional Superconductors and Superfluids (Springer, Berlin, 2001), p. 175.Google Scholar
  65. 65.
    N. B. Kopnin, A. S. Mel’nikov, V. I. Pozdnyakova, D. A. Ryzhov, I. A. Shereshevskii, and V. M. Vinokur, Phys. Rev. Lett. 95, 197002 (2005).ADSCrossRefGoogle Scholar
  66. 66.
    N. B. Kopnin, A. S. Mel’nikov, V. I. Pozdnyakova, D. A. Ryzhov, I. A. Shereshevskii, and V. M. Vinokur, Phys. Rev. B 75, 024514 (2007).ADSCrossRefGoogle Scholar
  67. 67.
    A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964).Google Scholar
  68. 68.
    A. S. Mel’nikov, D. A. Ryzhov, and M. A. Silaev, Phys. Rev. B 78, 064513 (2008).ADSCrossRefGoogle Scholar
  69. 69.
    A. S. Mel’nikov and M. A. Silaev, JETP Lett. 83, 578 (2006).CrossRefGoogle Scholar
  70. 70.
    H. F. Hess, R. B. Robinson, and J. V. Waszczak, Phys. Rev. Lett. 64, 2711 (1990).ADSCrossRefGoogle Scholar
  71. 71.
    I. Guillamon, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodiere, Phys. Rev. Lett. 101, 166407 (2008).ADSCrossRefGoogle Scholar
  72. 72.
    T. Cren, L. Serrier-Garcia, F. Debontridder, and D. Roditchev, Phys. Rev. Lett. 107, 097202 (2011).ADSCrossRefGoogle Scholar
  73. 73.
    N. Schopohl and K. Maki, Phys. Rev. B 52, 490 (1995).ADSCrossRefGoogle Scholar
  74. 74.
    N. Schopohl, arXiv:9804064 (1998).Google Scholar
  75. 75.
    L. Kramer and W. Pesch, Z. Phys. 269, 59 (1974).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Physics of MicrostructuresRussian Academy of SciencesNizhny NovgorodRussia
  2. 2.Lobachevskii State UniversityNizhny NovgorodRussia

Personalised recommendations