Superconducting states in frustrating t-J model:: A model connecting high-Tc cuprates, organic conductors and NaxCoO2

A two-dimensional t-J model on a frustrating lattice is studied using mean-field variational theories with Gutzwiller approximation. We find that a superconducting state with broken time-reversal symmetry (d+id state) is realized in the parameter region close to the triangular lattice. The frustration enlarges the region of superconductivity when t < 0 for the hole-doped case, which is equivalent to t > 0 for electron doping. We also discuss SU(2) degeneracy at half-filling. The d+id state probably corresponds to the spin gap state at half-filling.