Layered cobalt oxyhydrate as a heavy-fermion compound with extreme type-II superconductivity

We report the electrical, magnetic and thermal measurements on a layered cobalt oxyhydrate Na$_{0.31}$CoO$_{2}\cdot$1.3H$_{2}$O. Bulk superconductivity at 4.3 K is observed, however, the measured superconducting fraction is relatively low probably due to the sample's intrinsic two-dimensional characteristic. The compound exhibits extreme type-II superconductivity with the Ginzburg-Landau parameters $\kappa$ of about 140. The normal-state electronic specific heat coefficient is as large as 159 mJ/K$^{2}$$\cdot$mol, indicating heavy mass for the charge carriers. The electronic specific heat data in the superconducting state obey a power-law dependence, suggesting point-node or line-node for the superconducting gap structure.