Pairing correlation functions in the triangulart−Jmodel:d-wave andf-wave superconductivity

Abstract

Equal-time pairing correlation functions of the two-dimensional $t\text{\ensuremath{-}}J$ 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 $T\ensuremath{\sim}0.2t$, and find the growth of pairing correlations. When $tg0$ with hole doping, a rapid growth of effective $d$-wave pairing interaction is found that indicates the resonating-valence-bond superconductivity. In contrast, when $tl0$, 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 $T\ensuremath{\rightarrow}0$ 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, ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}∙y{\mathrm{H}}_{2}\mathrm{O}$, is discussed.