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VOLUME 85 (2007) | ISSUE 10 | PAGE 621
Superconductor-insulator duality for the array of Josephson wires
PACS: 74.40.+k, 74.81.Fa
Abstract
We propose novel model system for the studies of superconductor-insulator transitions, which is a regular lattice, whose each link consists of Josephson-junction chain of N \gg 1 junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy EJ large compared to the junctions's Coulomb energy EC = e2/2C. Exact duality transformation is derived, which transforms the Hamiltonian of the proposed model into a standard Hamiltonian of JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter q \approx N^2 \exp(-\sqrt{8E_J/E_C}), with superconductive state corresponding to small q < qc . The values of qc are calculated for magnetic frustrations f= 0 and f=1/2. Temperature of superconductive transition Tc(q) and q < qc is estimated for the same values of f. In presence of strong random offset charges, the T=0 phase diagram is controlled by the parameter \bar{q} = q/\sqrt{N}; we estimated critical value \bar{q}_c and critical temperature T_c(\bar{q} < \bar{q}_c) at zero magnetic frustration.