Competition between singlet and triplet pairings in NaxCoO2 center dot y H2O

We discuss the pairing symmetry of a cobaltate superconductor NaxCoO2.y H2O by adopting an effective single-band model that takes into account the e(g)(') hole pockets, as discussed in our previous paper [Phys. Rev. Lett. 93, 077001 (2004)]. Here we consider the off-site repulsions in addition to the on-site repulsion considered in our previous study. We show that the spin-triplet f-wave pairing proposed in our previous study is robust to some extent even in the presence of off-site repulsions. However, f-wave pairing gives way to singlet pairings for sufficiently large values of off-site repulsions. Among the singlet pairings, i-wave and extended s-wave pairings are good candidates which do not break time reversal symmetry below T-c in agreement with the experiments.