Phase transitions in a disordered granular superconductor near percolation

Abstract

The properties of a disordered granular superconductor consisting of superconducting grains of size comparable to the zero-temperature bulk superconducting coherence length embedded in a nonsuperconducting host are studied by means of a randomly diluted Josephson tunnel junction model near a percolation threshold $p_c$. A replicated (n→0) continuum Landau-Ginzburg field theory describing the macroscopic properties of this material is derived from first principles. The mean-field phase diagram as a function of temperature T, applied magnetic field H, and grain concentration p exhibits a Meissner phase, an Abrikosov vortex lattice, and a spin-glass phase all arising from the low-temperature phase coherence of the condensate wave function among the grains. For H=0, in the superconducting phase, the macroscopic superfluid density ${\rho }_s$∼(p-$p_c$ ${)}^t$ as p→$p_c$ where t=3 in mean-field theory. The spin-glass phase arises from frustration among loops of the percolating network in the presence of an applied magnetic field. Here ${\rho }_s$=0, leading to complete flux penetration on average but with a frozen-in distribution of randomly oriented tunneling supercurrents leading to power-law decaying ∼$x^{\mathrm{-}\left(d\mathrm{-}2\right)}$ local fluctuations in the B field. In the low-temperature limit, vortices are shown to consist of spin-glass cores in a superconducting background.