Studies of doping and temperature dependences of superfluid weight and   spectral function; Universal scaling behavior of pseudogap
  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. 
Sung-Sik Lee and Sung-Ho Suck Salk