Pairing correlation functions in the triangular t-J model: d-wave and f-wave superconductivity

Equal-time pairing correlation functions of the two-dimensional t-J model on the triangular lattice are studied using high-temperature expansions method. We calculate the pairing correlation lengths and the effective pairing interactions down to T∼0.2t, and find the growth of pairing correlations. When t>0 with hole doping, a rapid growth of effective d-wave pairing interaction is found that indicates the resonating-valence-bond superconductivity. In contrast, when t<0, where the ferromagnetic correlation and antiferromagnetic correlation compete, correlation lengths of triplet pairings as well as d-wave pairing grow at low temperatures, although they do not diverge for T→0 in the competing region, i.e., near half-filling. On the other hand, around n=0.4, f-wave pairing correlation tends to diverge, although its effective interaction is small. Relation of the present study to the recently discovered superconductor, NaxCoO2yH2O, is discussed.