Advertisement

JETP Letters

, Volume 85, Issue 10, pp 513–518 | Cite as

Superconductor-insulator duality for an array of Josephson wires

  • I. V. Protopopov
  • M. V. Feigel’man
Condensed Matter

Abstract

A novel model system is proposed for the study of superconductor-insulator transitions that is a regular lattice whose each link consists of a Josephson-junction chain of N ≫ 1 junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy E J larger compared to the Coulomb energy E C = e 2/2C of the junctions. An exact duality transformation is derived that transforms the Hamiltonian of the proposed model into a standard Hamiltonian of a JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter qN 2 exp\(( - \sqrt {8E_J /E_C } )\) with the superconductive state corresponding to small q < q c . The values of q c are calculated for magnetic frustrations f = 0 and f = 1/2. The temperature of the superconductive transition T c (q) and q < q c is estimated for the same values of f. In the presence of strong random offset charges, the T = 0 phase diagram is controlled by the parameter \(\bar q = q/\sqrt N \); the critical value \(\bar q_c \) and the critical temperature \(T_c (\bar q < \bar q_c )\) at zero magnetic frustration are estimated.

PACS numbers

74.40.+k 74.81.Fa 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Fazio and H. S. J. van der Zant, Phys. Rep. 355, 235 (2001).zbMATHCrossRefADSGoogle Scholar
  2. 2.
    M.P.A. Fisher, Phys. Rev. Lett. 65, 923 (1990); R. Fazio and G. Schoen, Phys. Rev. B 43, 5307 (1991).CrossRefADSGoogle Scholar
  3. 3.
    K. A. Matveev, A. I. Larkin, and L. I. Glazman, Phys. Rev. Lett. 89, 096802 (2002).Google Scholar
  4. 4.
    M. V. Feigel’man, S. E. Korshunov, and A. V. Pugachev, Pis’ma Zh. Éksp. Teor. Fiz. 65, 541 (1997) [JETP Lett. 65, 566 (1997)].ADSGoogle Scholar
  5. 5.
    J. G. Kissner and U. Eckern, Z. Phys. B 91, 155 (1993).CrossRefGoogle Scholar
  6. 6.
    A. van Otterlo, R. Fazio, and G. Schoen, Physica B (Amsterdam) 203, 504 (1994).ADSGoogle Scholar
  7. 7.
    C. Rojas and J. V. Jose, Phys. Rev. B 54, 12 361 (1996).Google Scholar
  8. 8.
    R. Fazio, A. van Otterlo, G. Schon, et al., Helv. Phys. Acta 65, 228 (1991).Google Scholar
  9. 9.
    I. V. Protopopov and M. V. Feigel’man (in preparation).Google Scholar
  10. 10.
    Y. Saito and H. Mueller-Krumbhaar, Phys. Rev. B 23, 308 (1981).CrossRefADSGoogle Scholar
  11. 11.
    G. S. Grest, Phys. Rev. B 39, 9267 (1989).CrossRefADSGoogle Scholar
  12. 12.
    P. Olsson, Phys. Rev. B 55, 3585 (1997).CrossRefADSGoogle Scholar
  13. 13.
    C. Christiansen, L. M. Hernandez, and A. M. Goldman, Phys. Rev. Lett. 88, 037004 (2002).Google Scholar
  14. 14.
    G. Sambandamurthy, L. W. Engel, A. Johansson, et al., Phys. Rev. Lett. 94, 017003 (2005).Google Scholar
  15. 15.
    M. V. Feigel’man and L. B. Ioffe, Phys. Rev. Lett. 74, 3447 (1995).CrossRefADSGoogle Scholar
  16. 16.
    H. G. Katzgraber, Phys. Rev. B 67, 180402 (2003); M. Nikolaou and M. Wallin, Phys. Rev. B 69, 184512 (2004).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • I. V. Protopopov
    • 1
    • 2
  • M. V. Feigel’man
    • 1
    • 2
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudny, Moscow regionRussia

Personalised recommendations