Instability of granular superconductivity

It is shown that bulk superconductivity of a three-dimensional granular metal can become unstable with respect to the diverging zero-point phase fluctuations which result from grain charging. A model of Josephson-coupled superconducting grains is used to calculate the effect of charging energy on the average order parameter at $T=0\mathrm{}$. In the mean-field approximation this system exhibits a second-order transition to normal state at a certain critical value of the ratio of the Josephson-coupling constant to the charging energy. The self-consistent harmonic approximation is shown to yield a spurious first-order transition.