Doped t-J Model on a Triangular Lattice: Possible Application to Na${}_x$CoO${}_2\cdot y$H${}_2$0 and Na${}_{1-x}$TiO${}_2$

We report the finding of time-reversal-symmetry-breaking $d_{x^2-y^2}+ id_{xy}$ superconducting ground state in the slave-boson mean-field theory for the t-J model on triangular lattice. For $t\mathrm{/}J=-5$ ($t\mathrm{/}J=-9$) pairing exists for $x<13$ ($x<8$) upon electron doping, and $x<56$ ($x<13$) upon hole doping. These results are potentially relevant to doped Mott insulators Na${}_x$CoO${}_2$.yH${}_2$O and Na${}_{1-x}$TiO${}_2$.