Abstract
We consider a general d-wave superconducting gap function in the presence of coexisting antiferromagnetic (AFM) long-range order. We find that the d-wave order parameter develops additional nodes without lowering the symmetry of the state due to the interplay of the superconducting and AFM correlations. This AFM correlated d-wave gap has a small gap structure inside the generic d-wave gap. As a result of this additional structure it shows quite a different response to impurities compared to a standard d-wave gap. We calculate the nuclear spin-lattice relaxation rate ${1/T}_{1}$ of this gap in the presence of impurities and discuss the implications for the experiments of some AFM heavy-fermion superconductors, in particular CeRhIn5.
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