Enhanced d-wave Superconducting Fluctuations in the 2D t-J model

I have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D $t$-$J$ model with $s$-, $d_{x^2-y^2}$ and $d_{xy}$-symmetry pairs. The strengths of the different symmetry correlations are measured using ${\bf q}=0$ correlation lengths. I find that for $J/t=0.4$ the correlation length for $d_{x^2-y^2}$ pairing grows strongly with decreasing temperature, developing a broad peak around doping $\delta=0.25$ when the temperature is reduced to $T/J=0.25$. The correlation lengths for $s$ and $d_{xy}$ pairs remain small and do not display peaks as a function of doping. The temperature scale for growth in the $d_{x^2-y^2}$ correlation length agrees with the temperature scale where the temperature derivative of the momentum distribution function $dn_{\bf k}/dT$ and the gradient of the momentum distribution function $|\nabla_{\bf k}n_{\bf k}|$ develop peaks on the Brillouin zone diagonal. This indicates that the low energy excitations in the 2D $t$-$J$ model are concentrated near the zone diagonal, as would be expected for superconducting order with $d_{x^2-y^2}$-symmetry pairs. I will also discuss differences between my calculation and previous calculations for superconducting correlations in the 2D $t$-$J$ model.