(M=Co,Rh)*

The heavy-fermion CeMIn5 family with M = Co, Rh provide a paradigm example of strange superconductivity with d−wave pairing and a non-Fermi liquid (strange metal, SM) normal state, emerged near an antiferromagnetic quantum critical point (QCP). The microscopic mechanism of strange superconductivity as well as its link to quantum criticality and strange metal behaviour are still long-standing un-resolved open issues. Recent ARPES and STM measurements indicate important roles played by both Kondo hybridization and antiferromagnetic fluctuations among f−electrons. We offer a microscopic mechanism to address these issues based on a competition and coexistence between Kondo hybridization and antiferromagnetic resonanting valence-bond (RVB) spin liquid in the Kondo-Heisenberg model on a quasi-2d lattice. The competition between the two leads to a Kondo breakdown QCP, while the co-existence gives rise to superconductivity. Our results via a large-N mean-field and effective field theory combined with renormalization group approaches explain remarkably well the observed normal state SM behaviors near criticality and how superconductivity is developed from it.