Correlation between Superconducting Transition Temperature $T_c$ and   Increase of Nuclear Spin-Lattice Relaxation Rate Devided by Temperature   $1/T_1T$ at $T_c$ in the Hydrate Cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O
  We have performed Co-nuclear quadrupole resonance (NQR) studies on Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O compounds with different Na ($x$) and hydrate ($y$) contents. Two samples with different Na contents but nearly the same $T_c$ values ($x$ = 0.348, $T_c$ = 4.7 K ; $x$ = 0.339, $T_c$ = 4.6 K) were investigated. The spin-lattice relaxation rate $1/T_1$ in the superconducting (SC) and normal states is almost the same for the two samples except just above $T_c$. NQR measurements were also performed on different-hydrate-content samples with different $T_c$ values, which were prepared from the same Na-content ($x$ = 0.348) sample. From measurements of $1/T_1$ using the different-hydrate-content samples, it was found that a low-$T_c$ sample with $T_c = 3.9$ K has a larger residual density of states (DOS) in the SC state and a smaller increase of $1/T_1T$ just above $T_c$ than a high-$T_c$ sample with $T_c$ = 4.7 K. The former behavior is consistent with that observed in unconventional superconductors, and the latter suggests the relationship between $T_c$ and the increase in DOS just above $T_c$. This increase, which is seemingly associated with the two-dimensionality of the CoO$_2$ plane, is considered to be one of the most important factors for the occurrence of superconductivity. 
Y. Ihara, K. Ishida, C. Michioka, M. Kato, K. Yoshimura, K. Takada, T.   Sasaki, H. Sakurai, and E. Takayama-Muromachi