  Using the improved U(1) and SU(2) slave-boson approaches of the t-J
Hamiltonian that we developed recently, we study the doping and temperature
dependence of superfluid weight and spectral function and discuss our finding
of the universal scaling behavior of pseudogap. It is shown that at low hole
doping concentrations and at low temperatures there exists a propensity of a
linear decrease in the superfluid weight with temperature, and a tendency of
doping independence in the linearly decreasing slopes of the superfluid weight
with temperature in qualitative agreement with the experiments. It is also
demonstrated that there exists the boomerang behavior, that is, both Tc and the
superfluid weight increase with hole doping concentration x in the underdoped
region, reaches a saturation(maximum) at a hole doping above optimal doping and
decreases beyond the saturation point in the overdoped region in agreement with
mu-SR measurements. We further investigate the doping and temperature
dependence of spectral function and discuss our theoretical finding of a
scaling behavior of pseudogap. In addition we discuss the cause of hump and
quasi-particle peak in the observed spectral functions of high Tc cuprates. It
is demonstrated that the sharpening of the observed quasi-particle peak below
Tc is attributed to the bose condensation of holon pair in agreement with
observations. From the predicted ratios of pseudogap to both the
superconducting temperature Tc and the pseudogap temperature T* respectively as
a function of hole doping concentration x, we find that there exists a
universal scaling behavior (sample independence) of these ratios with doping,
by showing a nonlinearly decreasing behavior of the former and a near doping
independence of the latter.
