Magnetic penetration length and irreversibility of a disordered granular superconductor withπjunctions

Abstract

We calculate the magnetic penetration length $\ensuremath{\lambda}(T)$ of a disordered granular superconductor with $\ensuremath{\pi}$ 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 ${J}_{0}g0,$ with width J. For disorder strength $\ensuremath{\delta}\ensuremath{\equiv}{J/J}_{0}l1$ 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 $\ensuremath{\delta}$ near 1 there is a further possibility of reentry into a low-temperature normal glass phase. For $\ensuremath{\delta}g~1$ 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.