Critical magnetic fluctuations induced superconductivity and residual   density of states in $CeRhIn_5$ superconductor
  We propose the multiband extension of the spin-fermion model to address the superconducting d-wave pairing due to magnetic interaction near critical point. We solve the unrestricted gap equation with a general d-wave symmetry gap and find that divergent magnetic correlation length $\xi$ leads to the very unharmonic shape of the gap function with shallow gap regions near nodes. These regions are extremely sensitive to disorder. Small impurity concentration induces substantial residual density of states. We argue that we can understand the large $N_{res}(0) = \lim_{T\to 0} C_p(T)/T$ value and its pressure dependence of the recently discovered $CeRhIn_5$ superconductor under pressure within this approach. 
Yunkyu Bang, I. Martin and A.V. Balatsky