Superfluid Weight, Free Carrier Density, and Specific Heat of the d=3 tJ Model at Finite Temperatures

The superfluid weight, free carrier density, and specific heat of the three-dimensional tJ model are calculated by renormalization-group theory. We find that optimal hole doping for superfluidity occurs in the electron density range of n_i approximately between 0.63 - 0.68, where the superfluid weight n_s/m* reaches a local maximum. This density range is within the novel tau phase, where the electron hopping strength renormalizes to infinity, the system remains partially filled at all length scales, and the electron-hopping expectation value remains distinctively non-zero at all length scales. The calculated superfluid weight drops off sharply in the overdoped region. Under hole doping, the calculated density of free carriers increases until optimal doping and remains approximately constant in the overdoped region, as seen experimentally in high-T_c materials. Furthermore, from calculation of the specific heat coefficient gamma, we see clear evidence of a gap in the excitation spectrum for the tau phase.