Skip to main content
SpringerLink
Log in

Vortex matter in low-dimensional systems with proximity-induced superconductivity

  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

We theoretically study the vortex matter structure in low-dimensional systems with superconducting order induced by proximity to a bulk superconductor. We analyze the effects of microscopic coupling mechanisms between the two systems and the effects of possible mismatch in the band structures of these materials on the energy spectrum of vortex-core electrons. The unusual structure of vortex cores is discussed in the context of recent tunneling microscopy/spectroscopy experiments.

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. W. L. McMillan, Phys. Rev. 175, 537 (1968).

    Article  ADS  Google Scholar 

  2. P. G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, New York, 1989).

    Google Scholar 

  3. C. W. J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008).

    Article  ADS  Google Scholar 

  4. A. H. Castro Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).

    Article  ADS  Google Scholar 

  5. M. Kociak, A. Yu. Kasumov, S. Guéron, B. Reulet, I. I. Khodos, Yu. B. Gorbatov, V. T. Volkov, L. Vaccar- ini, and H. Bouchiat, Phys. Rev. Lett. 86, 2416 (2001).

    Article  ADS  Google Scholar 

  6. J. C. Charlier, X. Blase, and S. Roche, Rev. Mod. Phys. 79, 677 (2007).

    Article  ADS  Google Scholar 

  7. Xiao-Liang Qi and Shou-Cheng Zhang, Rev. Mod. Phys. 83, 1057 (2011).

    Article  ADS  Google Scholar 

  8. H. B. Heersche, P. Jarillo-Herrero, J. B. Oostinga, L. M. K. Vandersypen, and A. F. Morpurgo, Solid State Commun. 143, 72 (2007)

    Article  ADS  Google Scholar 

  9. L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).

    Article  ADS  Google Scholar 

  10. J. Alicea, Rep. Prog. Phys. 75, 076501 (2012).

    Article  ADS  Google Scholar 

  11. H. F. Hess, R. B. Robinson, R. C. Dynes, J. M. Valles, Jr., and J. V. Waszczak, Phys. Rev. Lett. 62, 214 (1989); H. F. Hess, R. B. Robinson, and J. V. Waszczak, Phys. Rev. Lett. 64, 2711 (1990); I. Guillamon, H. Suderow, S. Vieira, L. Cario, P. Diener, and P. Rodiere, Phys. Rev. Lett. 101, 166407 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  13. A. Kastalsky, A. W. Kleinsasser, L. H. Greene, R. Bhat, F. P. Milliken, and J. P. Harbison, Phys. Rev. Lett. 67, 3026 (1991); D. Quirion, C. Hoffmann, F. Lefloch, and M. Sanquer, Phys. Rev. B: Condens. Matter 65, 100508(R) (2002).

    Article  ADS  Google Scholar 

  14. B. J. van Wees, P. de Vries, P. Magnee, and T. M. Klapwijk, Phys. Rev. Lett. 69, 510 (1992).

    Article  ADS  Google Scholar 

  15. A. F. Volkov, JETP Lett. 55(12), 746 (1992); A. F. Volkov, Physica B (Amsterdam) 203, 267 (1994).

    ADS  Google Scholar 

  16. A. F. Volkov, P. H. C. Magnée, B. J. van Wees, and T. M. Klapwijk, Physica C (Amsterdam) 242, 261 (1995).

    Article  ADS  Google Scholar 

  17. F. W. J. Hekking and Yu. V. Nazarov, Phys. Rev. B: Condens. Matter 49, 6847 (1994).

    Article  ADS  Google Scholar 

  18. N. B. Kopnin, Phys. Rev. B: Condens. Matter 57, 11775 (1998); A. S. Mel’nikov, Phys. Rev. Lett. 86, 4108 (2001).

    Article  ADS  Google Scholar 

  19. Ø. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and Ch. Renner, Rev. Mod. Phys. 79, 353 (2007).

    Article  ADS  Google Scholar 

  20. A. E. Koshelev and A. A. Golubov, Phys. Rev. Lett. 90, 177002 (2003).

    Article  ADS  Google Scholar 

  21. F. Giubileo, D. Roditchev, W. Sacks, R. Lamy, D. X. Thanh, J. Klein, S. Miraglia, D. Fruchart, J. Marcus, and Ph. Monod, Phys. Rev. Lett. 87, 177008 (2001).

    Article  ADS  Google Scholar 

  22. N. B. Kopnin and A. S. Melnikov, Phys. Rev. B: Condens. Matter 84, 064524 (2011).

    Article  ADS  Google Scholar 

  23. G. Fagas, G. Tkachov, A. Pfund, and K. Richter, Phys. Rev. B: Condens. Matter 71, 224510 (2005).

    Article  ADS  Google Scholar 

  24. J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Phys. Rev. B 82, 094522 (2010).

    Article  ADS  Google Scholar 

  25. A. L. Rakhmanov, A. V. Rozhkov, and Franco Nori, Phys. Rev. B: Condens. Matter 84, 075141 (2011); R. S. Akzyanov, A. V. Rozhkov, A. L. Rakhmanov, F. Nori, arXiv:cond-mat/1307.0923.

    Article  ADS  Google Scholar 

  26. P. A. Ioselevich, P. M. Ostrovsky, and M. V. Feigelman, Phys. Rev. B: Condens. Matter 86, 035441 (2012).

    Article  ADS  Google Scholar 

  27. N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford University Press, Oxford, 2001).

    Book  Google Scholar 

  28. A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Fizmatgiz, Moscow, 1962; Pergamon, London, 1965).

    Google Scholar 

  29. C. W. J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006).

    Article  ADS  Google Scholar 

  30. Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).

    Article  ADS  Google Scholar 

  31. E. Perfetto, Phys. Rev. Lett. 110, 087001 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. G. E. Volovik, JETP Lett. 57(4), 244 (1993); G. E. Volovik, The Universe in a Helium Droplet (Oxford University Press, Oxford, 2003).

    ADS  Google Scholar 

  34. K. Shiozaki, T. Fukui, and S. Fujimoto, Phys. Rev. B: Condens. Matter 86, 125405 (2012).

    Article  ADS  Google Scholar 

  35. N. Schopohl and K. Maki, Phys. Rev. B: Condens. Matter 52, 490 (1995).

    Article  ADS  Google Scholar 

  36. I. Maggio-Aprile, Ch. Renner, A. Erb, E. Walker, and Ø. Fischer, Phys. Rev. Lett. 75, 2754 (1995); B. W. Hoogenboom, Ch. Renner, B. Revaz, I. Maggio-Aprile, and Ø. Fischer, Physica C (Amsterdam) 332, 440 (2000); S. H. Pan, E. W. Hudson, A. K. Gupta, K.-W. Ng, H. Eisaki, S. Uchida, and J. C. Davis, Phys. Rev. Lett. 85, 1536 (2000).

    Article  ADS  Google Scholar 

  37. L. P. Gor’kov and N. B. Kopnin, Sov. Phys. JETP 38(1), 195 (1974).

    ADS  Google Scholar 

  38. A. Berman, and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, United States, 1994).

    Book  MATH  Google Scholar 

  39. A. A. Golubov, Czech. J. Phys. 46, 569 (1996).

    Article  Google Scholar 

  40. M. Yu. Kupriyanov, Sverkhprovodimost: Fiz., Khim., Tekh. 2, 5 (1989).

    Google Scholar 

  41. A. A. Golubov and U. Hartmann, Phys. Rev. Lett. 72, 3602 (1994).

    Article  ADS  Google Scholar 

  42. M. R. Eskildsen, M. Kugler, S. Tanaka, J. Jun, S. M. Kazakov, J. Karpinski, and Ø. Fischer, Phys. Rev. Lett. 89, 187003 (2002).

    Article  ADS  Google Scholar 

  43. A. D. Beyer, M. S. Grinolds, M. L. Teague, S. Tajima, and N.-C. Yeh, Europhys. Lett. 87, 37005 (2009).

    Article  ADS  Google Scholar 

  44. R. Jackiw and P. Rossi, Nucl. Phys. B 190, 681 (1981).

    Article  ADS  Google Scholar 

  45. D. L. Bergman and K. L. Hur, arXiv:cond-mat//0806.0379.

  46. I. M. Khaymovich, N. B. Kopnin, A. S. Mel’nikov, and I. A. Shereshevskii, Phys. Rev. B: Condens. Matter 79, 224506 (2009).

    Article  ADS  Google Scholar 

  47. A. S. Mel’nikov and M. A. Silaev, JETP Lett. 83(12), 578 (2006).

    Article  Google Scholar 

  48. 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); A. S. Mel’nikov, D. A. Ryzhov, and M. A. Silaev, Phys. Rev. B: Condens. Matter 78, 064513 (2008).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lounasmaa Laboratory, Aalto University, P.O. Box 15100, 00076, Aalto, Finland

    N. B. Kopnin

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 117940, Russia

    N. B. Kopnin

  3. Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhni Novgorod, 603950, Russia

    I. M. Khaymovich & A. S. Mel’nikov

Authors
  1. N. B. Kopnin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. M. Khaymovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Mel’nikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. B. Kopnin.

Additional information

Dedicated to the memory of Professor Anatoly Larkin

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kopnin, N.B., Khaymovich, I.M. & Mel’nikov, A.S. Vortex matter in low-dimensional systems with proximity-induced superconductivity. J. Exp. Theor. Phys. 117, 418–438 (2013). https://doi.org/10.1134/S1063776113110113

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776113110113

Keywords

Search

Navigation