Skip to main content
SpringerLink
Log in

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

  • Order, Disorder, and Phase Transition in Condensed System
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

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 T ≪ T 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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Campbell and J. E. Evetts, Critical Currents in Superconductors (Taylor and Francis, London, 1972).

    Google Scholar 

  2. 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 

  3. P. Yang and Ch. M. Lieber, Science 273, 1836 (1996).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  5. A. F. Hebard, A. T. Fiory, and S. Somekh, IEEE Trans. Magn. 1, 589 (1977).

    Article  ADS  Google Scholar 

  6. A. N. Lykov, Solid State Commun. 86, 531 (1993).

    Article  ADS  Google Scholar 

  7. M. Baert, V. V. Metlushko, R. Jonckheere, V. V. Moshchalkov, and Y. Bruynseraede, Phys. Rev. Lett. 74, 3269 (1995).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  10. C. P. Bean and J. D. Livingston, Phys. Rev. Lett. 12, 14 (1971).

    Article  ADS  Google Scholar 

  11. G. S. Mkrtchyan and V. V. Shmidt, Sov. Phys. JETP 34, 195 (1971).

    ADS  Google Scholar 

  12. M. Tinkham, Introduction to Superconductivity (Dover, New York, 2004; Atomizdat, Moscow, 1980).

    Google Scholar 

  13. H. Nordborg and V. M. Vinokur, Phys. Rev. B 62, 12408 (2000).

    Article  ADS  Google Scholar 

  14. A. Buzdin and D. Feinberg, Phys. C (Amsterdam, Neth.) 256, 303 (1996).

    Article  ADS  Google Scholar 

  15. A. Buzdin and M. Daumens, Phys. C (Amsterdam, Neth.) 294, 257 (1998).

    Article  ADS  Google Scholar 

  16. A. Buzdin and M. Daumens, Phys. C (Amsterdam, Neth.) 332, 108 (2000).

    Article  ADS  Google Scholar 

  17. A. A. Bespalov and A. S. Melnikov, Supercond. Sci. Technol. 26, 085014 (2013).

    Article  ADS  Google Scholar 

  18. S. M. Maurer, N.-C. Yeh, and T. A. Tombrello, Phys. Rev. B 54, 15372 (1996).

    Article  ADS  Google Scholar 

  19. S. M. Maurer, N.-C. Yeh, and T. A. Tombrello, J. Phys.: Condens. Matter 10, 7429 (1998).

    ADS  Google Scholar 

  20. D. J. Priour, Jr. and H. A. Fertig, Phys. Rev. B 67, 054504 (2003).

    Article  ADS  Google Scholar 

  21. B. Rosenstein, I. Shapiro, and B. Ya. Shapiro, Phys. Rev. B 81, 064507 (2010).

    Article  ADS  Google Scholar 

  22. N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Clarendon, Oxford, 2001).

    Book  Google Scholar 

  23. C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Lett. 9, 307 (1964).

    Article  ADS  Google Scholar 

  24. F. Guinea and Yu. Pogorelov, Phys. Rev. Lett. 74, 462 (1995).

    Article  ADS  Google Scholar 

  25. M. V. Feigel’man and M. A. Skvortsov, Phys. Rev. Lett. 78, 2640 (1997).

    Article  ADS  Google Scholar 

  26. M. A. Skvortsov, D. A. Ivanov, and G. Blatter, Phys. Rev. B 67, 014521 (2003).

    Article  ADS  Google Scholar 

  27. A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998).

    Article  ADS  Google Scholar 

  28. A. A. Koulakov and A. I. Larkin, Phys. Rev. B 59, 12021 (1999).

    Article  ADS  Google Scholar 

  29. N. B. Kopnin, Phys. Rev. B 60, 581 (1999).

    Article  ADS  Google Scholar 

  30. E. V. Thuneberg, J. Kurkijarvi, and D. Rainer, Phys. Rev. Lett. 48, 1853 (1982).

    Article  ADS  Google Scholar 

  31. E. V. Thuneberg, J. Kurkijarvi, and D. Rainer, Phys. Rev. B 29, 3913 (1984).

    Article  ADS  Google Scholar 

  32. A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 28, 1200 (1968).

    ADS  Google Scholar 

  33. G. Eilenberger, Z. Phys. 214, 195 (1968).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. E. V. Thuneberg, J. Low Temp. Phys. 62, 27 (1986).

    Article  ADS  Google Scholar 

  36. M. Friesen and P. Muzikar, Phys. Rev. B 53, R11953 (1986).

    Article  ADS  Google Scholar 

  37. A. S. Mel’nikov, A. V. Samokhvalov, and M. N. Zubarev, Phys. Rev. B 79, 134529 (2009).

    Article  ADS  Google Scholar 

  38. B. Rosenstein, I. Shapiro, E. Deutch, and B. Ya. Shapiro, Phys. Rev. B 84, 134521 (2011).

    Article  ADS  Google Scholar 

  39. N. N. Bogolyubov, Sov. Phys. JETP 7, 41 (1958).

    Google Scholar 

  40. P. G. de Gennes, Superconductivity of Metals and Alloys (Bengamin, New York, 1966; Mir, Moscow, 1968).

    MATH  Google Scholar 

  41. A. S. Mel’nikov, A. V. Samokhvalov, and V. L. Vadimov, JETP Lett. 102, 775 (2015).

    Article  ADS  Google Scholar 

  42. V. L. Vadimov and A. S. Mel’nikov, J. Low Temp. Phys. 183, 342 (2016).

    Article  ADS  Google Scholar 

  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. A. S. Mel’nikov and A. V. Samokhvalov, JETP Lett. 94, 759 (2011).

    Article  Google Scholar 

  45. P. A. Ioselevich and M. V. Feigel’man, Phys. Rev. Lett. 106, 077003 (2011).

    Article  ADS  Google Scholar 

  46. P. A. Ioselevich, P. M. Ostrovsky, and M. V. Feigel’man, Phys. Rev. B 86, 035441 (2012).

    Article  ADS  Google Scholar 

  47. A. L. Rakhmanov, A. V. Rozhkov, and F. Nori, Phys. Rev. B 84, 075141 (2011).

    Article  ADS  Google Scholar 

  48. R. S. Akzyanov, A. V. Rozhkov, A. L. Rakhmanov, and F. Nori, Phys. Rev. B 89, 085409 (2014).

    Article  ADS  Google Scholar 

  49. G. Karapetrov, J. Fedor, M. Iavarone, D. Rosenmann, and W. K. Kwok, Phys. Rev. Lett. 95, 167002 (2005).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  51. A. V. Silhanek, S. Raedts, M. J. Van Bael, and V. V. Moshchalkov, Phys. Rev. B 70, 054515 (2004).

    Article  ADS  Google Scholar 

  52. A. I. Buzdin, Phys. Rev. B 47, 11416 (1993).

    Article  ADS  Google Scholar 

  53. V. A. Schweigert, F. M. Peeters, and P. S. Deo, Phys. Rev. Lett. 81, 2783 (1998).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  55. A. Bezryadin, A. Buzdin, and B. Pannetier, Phys. Lett. A 195, 373 (1994).

    Article  ADS  Google Scholar 

  56. G. E. Volovik, JETP Lett. 57, 244 (1993).

    ADS  Google Scholar 

  57. Y. Tanaka, S. Kashiwaya, and H. Takayanagi, Jpn. J. Appl. Phys. 34, 4566 (1995).

    Article  ADS  Google Scholar 

  58. D. Rainer, J. A. Sauls, and D. Waxman, Phys. Rev. B 54, 10094 (1993).

    Article  ADS  Google Scholar 

  59. A. S. Mel’nikov and V. M. Vinokur, Nature 415, 60 (2002).

    Article  ADS  Google Scholar 

  60. A. S. Mel’nikov and V. M. Vinokur, Phys. Rev. B 65, 224514 (2002).

    Article  ADS  Google Scholar 

  61. A. S. Mel’nikov, D. A. Ryzhov, and M. A. Silaev, Phys. Rev. B 78, 064513 (2008).

    Article  ADS  Google Scholar 

  62. S. M. M. Virtanen and M. M. Salomaa, Phys. Rev. B 60, 145581 (1999).

    Article  Google Scholar 

  63. M. A. Silaev and V. A. Silaeva, J. Phys.: Condens. Matter 25, 225702 (2013).

    ADS  Google Scholar 

  64. M. Eschrig, D. Rainer, and J. A. Sauls, Vortices in Unconventional Superconductors and Superfluids (Springer, Berlin, 2001), p. 175.

    Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  67. A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964).

    Google Scholar 

  68. A. S. Mel’nikov, D. A. Ryzhov, and M. A. Silaev, Phys. Rev. B 78, 064513 (2008).

    Article  ADS  Google Scholar 

  69. A. S. Mel’nikov and M. A. Silaev, JETP Lett. 83, 578 (2006).

    Article  Google Scholar 

  70. H. F. Hess, R. B. Robinson, and J. V. Waszczak, Phys. Rev. Lett. 64, 2711 (1990).

    Article  ADS  Google Scholar 

  71. I. Guillamon, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodiere, Phys. Rev. Lett. 101, 166407 (2008).

    Article  ADS  Google Scholar 

  72. T. Cren, L. Serrier-Garcia, F. Debontridder, and D. Roditchev, Phys. Rev. Lett. 107, 097202 (2011).

    Article  ADS  Google Scholar 

  73. N. Schopohl and K. Maki, Phys. Rev. B 52, 490 (1995).

    Article  ADS  Google Scholar 

  74. N. Schopohl, arXiv:9804064 (1998).

    Google Scholar 

  75. L. Kramer and W. Pesch, Z. Phys. 269, 59 (1974).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, 603950, Russia

    A. V. Samokhvalov & A. S. Melnikov

  2. Lobachevskii State University, Nizhny Novgorod, 603950, Russia

    A. V. Samokhvalov & A. S. Melnikov

Authors
  1. A. V. Samokhvalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Melnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Samokhvalov.

Additional information

Original Russian Text © A.V. Samokhvalov, A.S. Melnikov, 2018, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 153, No. 2, pp. 268–282.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samokhvalov, A.V., Melnikov, A.S. Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity. J. Exp. Theor. Phys. 126, 224–236 (2018). https://doi.org/10.1134/S1063776118020048

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776118020048

Search

Navigation