  The heavy fermion CeMIn5 family with M = Co, Rh, Ir provide a prototypical
example of strange superconductors with unconventional d-wave pairing and
strange metal normal state, emerged near an antiferromagnetic quantum critical
point. The microscopic origin of strange superconductor and its link to
antiferromagnetic quantum criticality and strange metal state are still open
issues. We propose a microscopic mechanism for strange superconductor, based on
the coexistence and competition between the Kondo correlation and the quasi-2d
short-ranged antiferromagnetic resonating-valence-bond spin-liquid near the
antiferromagnetic quantum critical point via a large-N Kondo-Heisenberg model
and renormalization group analysis beyond the mean-field level. We find the
coexistence (competition) between the two types of correlations well explains
the overall features of superconducting and strange metal state. The interplay
of these two effects provides a qualitative understanding on how
superconductivity emerges from the SM state and the observed superconducting
phase diagrams for CeMIn5 near the anti-ferromagnetic quantum critical point.
