Abstract
We discuss the pairing symmetry of a cobaltate superconductor ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}y\phantom{\rule{0.3em}{0ex}}{\mathrm{H}}_{2}\mathrm{O}$ by adopting an effective single-band model that takes into account the ${e}_{g}^{\ensuremath{'}}$ 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.
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