Level statistics inside the core of a superconductive vortex

  • M. A. Skvortsov
  • M. V. Feigel’man
  • V. E. Kravtsov
Condensed Matter


A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ−1ω0∼Δ2/E F . At low energies εωTh∼ (ω0/τ)1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω0τ)]−1.

PACS numbers

74.60.Ec 74.25.Jb 74.80.Fp 


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  1. 1.
    K. B. Efetov, Supersymmetry in Disorder and Chaos, Cambridge Univ. Press, New York, 1997.Google Scholar
  2. 2.
    C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).CrossRefADSGoogle Scholar
  3. 3.
    A. Altland, B. Simons, and D. Taras-Semchuk, JETP Lett. 67, 22 (1998).CrossRefADSGoogle Scholar
  4. 4.
    F. Zhou, P. Charlat, B. Spivak, and B. Pannetier,
  5. 5.
    A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997).CrossRefADSGoogle Scholar
  6. 6.
    K. M. Frahm, P. W. Brouwer, J. A. Melsen, and C. W. J. Beenakker, Phys. Rev. Lett. 76, 2981 (1996).ADSGoogle Scholar
  7. 7.
    C. Caroli, P. G. de Gennes, and J. Matricon, Phys. Rev. Lett. 9, 307 (1964).Google Scholar
  8. 8.
    N. B. Kopnin and V. E. Kravtsov, JETP Lett. 23, 578 (1976); Zh. Éksp. Teor. Fiz. 71, 1644 (1976) [Sov. Phys. JETP 44, 861 (1976)].ADSGoogle Scholar
  9. 9.
    G. E. Volovik, JETP Lett. 57, 244 (1993); Zh. Éksp. Teor. Fiz. 104, 3070 (1993) [JETP 77, 435 (1993)].ADSGoogle Scholar
  10. 10.
    M. V. Feigel’man and M. A. Skvortsov, Phys. Rev. Lett. 78, 2640 (1997).ADSGoogle Scholar
  11. 11.
    A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998); A. I. Larkin and A. A. Koulakov, Scholar
  12. 12.
    M. A. Skvortsov, V. E. Kravtsov, and M. V. Feigel’man, in preparation.Google Scholar
  13. 13.
    A. D. Mirlin, Yan V. Fyodorov, F.-M. Dittes et al., Phys. Rev. E 54, 3221 (1996).CrossRefADSGoogle Scholar
  14. 14.
    A. G. Aronov, A. D. Mirlin, and P. Wölfle, Phys. Rev. B 49, 16609 (1994).Google Scholar
  15. 15.
    V. E. Kravtsov and A. D. Mirlin, JETP Lett. 60, 656 (1994).ADSGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 1998

Authors and Affiliations

  • M. A. Skvortsov
    • 1
  • M. V. Feigel’man
    • 1
  • V. E. Kravtsov
    • 1
    • 2
  1. 1.L. D. Landau Institute of Theoretical PhysicsMoscowRussia
  2. 2.International Center for Theoretical PhysicsTriesteItaly

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