  Recent experiments in quantum critical heavy fermion metals have pushed to
the fore the question about whether antiferromagnetic fluctuations can promote
both spin-singlet and spin-triplet superconductivity. Here we address the issue
through non-perturbative calculations in antiferromagnetically correlated Kondo
systems. We identify Kondo-destruction quantum critical points in both the
SU(2) symmetric and Ising-anisotropic cluster Bose-Fermi Anderson models. The
spin-singlet pairing correlations are significantly enhanced near the quantum
critical point in the SU(2) case; however, with adequate but still realistic
degree of Ising anisotropy, the spin-triplet pairing correlations are
competitive. Our results demonstrate that spin-flip processes strengthen the
spin-singlet pairing at the Kondo-destruction quantum critical points, and
point towards a way for antiferromagnetic correlations to drive spin-triplet
pairing. Further implications of our findings in the broader context of
strongly correlated superconductivity are discussed.
