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


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 


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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

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