Nuclear spin-lattice relaxation rate in the D+iD superconducting state: implications for CoO superconductor

We calculated the nuclear spin-lattice relaxation rate $1\mathrm{/}{T}_1$ for the D+iD superconducting state with impurities. We found that small amount of unitary impurities quickly produces the residual density of states inside the gap. As a result, the T-linear behavior in 1/T${}_1$ is observed at low temperatures. Our results show that the D+iD pairing symmetry of the superconducting state of Na${}_{0.35}$CoO${}_2\cdot y$H${}_2$ O is compatible with recent ${}^{59}$Co 1/T${}_1$ experiments of several groups.