Superfluid weight vs. superconducting temperature based on a U(1) slave-boson approach to the t-J Hamiltonian

Based on an improved U(1) slave-boson approach to the t-J Hamiltonian, we invest igate a relationship between the superfluid weight $n_s/m^*$(the superconducting charge carrier density/the effective mass of the charge carrier) and the superc onducting temperature $T_c$. From the present study we find a linear increase of $n_s/m^*$ with $T_c$ with th e doping concentration in the underdoped region, a saturation around the optimal doping and a decrease in both $n_s/m^*$ and $T_c$ in the overdoped region. Such a trend of the `boomerang' shaped locus in $n_s/m^*$ vs. $T_c$ with increas ing doping concentration from the underdoped to the heavily overdoped region is predicted to be in complete agreement with muon-spin-relaxation measurements. The boomerang behavior is found to occur in correlation with reduction in the sp in singlet pairing(spinon pairing) order in the heavily overdoped region.