Superconducting Properties under Magnetic Field in Na$_{0.35}$CoO$_{2}{cdot}1.3$H$_{2}$O Single Crystal

We report the in-plane resistivity and magnetic susceptibility of the layered cobalt oxide Na$_{0.35}$CoO$_{2}{cdot}1.3$H$_{2}$O single crystal. The temperature dependence of the resistivity shows metallic behavior from room temperature to the superconducting transition temperature $T_{c}$ of 4.5 K. Sharp resistive transition, zero resistivity and almost perfect superconducting volume fraction below $T_{c}$ indicate the good quality and the bulk superconductivity of the single crystal. The upper critical field $H_{c2}$ and the coherence length $xi$ are obtained from the resistive transitions in magnetic field parallel to the c-axis and the $ab$-plane. The anisotropy of $xi$, $xi_{ab} / xi_{c} =$ 12 nm/1.3 nm $simeq$ 9.2, suggests that this material is considered to be an anisotropic three dimensional superconductor. In the field parallel to the $ab$-plane, $H_{c2}$ seems to be suppressed to the value of Pauli paramagnetic limit. It may indicate the spin singlet superconductivity in the cobalt oxide.