Effects of disorder on the upper critical field in superconducting Na _0.35CoO₂yH₂O

The curvature of upper critical field (H_c2) for two-band superconductors is investigated based on the microscopic gap equation. By including effects of nonmagnetic impurity, it is shown that the observed upward curvature in hydrate cobaltate Na_0.35CoO₂yH₂O can be quantitatively reproduced by assuming a transition of the pairing symmetry from s-wave at low fields to d_x2-y2 + id_xy at high fields. Our results indicate that two different pairing symmetries must occur on different energy bands to account for the upward curvature. Furthermore, disorders are responsible for the suppression of upward curvature observed at low temperatures in experiments. These results provide important clues to understand superconductivity occurring in hydrate cobaltate.