  We study the non-local superconducting pairing of two interacting Anderson
impurities, which has an instability near the quantum critical point from the
competition between the Kondo effect and an antiferromagnetic inter-impurity
spin exchange interaction. As revealed by the dynamics over the whole energy
range, the superconducting pairing fluctuations acquire considerable strength
from an energy scale much higher than the characteristic spin fluctuation scale
while the low energy behaviors follow those of the staggered spin
susceptibility. We argue that the glue to the superconducting pairing is not
the spin fluctuations, but rather the effective Coulomb interaction. On the
other hand, critical spin fluctuations in the vicinity of quantum criticality
are also crucial to a superconducting pairing instability, by preventing a
Fermi liquid fixed point being reached to keep the superconducting pairing
fluctuations finite at low energies. A superconducting order, to reduce the
accumulated entropy carried by the critical degrees of freedom, may arise
favorably from this instability.
