Magnetic penetration length and irreversibility of a disordered granular superconductor with π junctions

We calculate the magnetic penetration length λ(T) of a disordered granular superconductor with π junctions in zero magnetic field, using a mean-field replica method. The superconductor is modeled by an array of Josephson junctions whose couplings are drawn randomly from a Gaussian distribution centered at J0>0, with width J. For disorder strength δ≡J/J0<1 there are three thermodynamical phases of the array separated by continuous transitions: (i) the high-temperature normal phase, (ii) the reversible superconducting phase, and (iii) the low-temperature superconducting glass phase with broken ergodicity. For a range of disorder δ near 1 there is a further possibility of reentry into a low-temperature normal glass phase. For δ≥1 there are only two phases: (i) the high-temperature normal phase and (ii) the low-temperature normal glass phase with broken ergodicity. In the superconducting glass phase we calculate both the Gibbs averaged and the single-state-averaged magnetic penetration lengths. copyright 1999 The American Physical Society