Characteristic temperatures of pseudo-gap phenomenon in the under-doped high temperature cuprate superconductors

The anomaly in the normal state of high-T-c superconductors is related to t he pseudo-gap phenomenon. For the under-doped cuprate superconductors, the relationship between the logarithmic increment in conductivity (w.r.t. the normal conductivity I/rho (N)(T)) and the inverse temperature exhibits some specific characters at temperatures T*, T-S and T-F The temperatures T* an d Ts are respectively the opening temperature and the terminating temperatu re for the cross over in the pseudo-gap phenomenon, while the temperature T F is close to the onset critical temperature of the superconductor. It is s hown experimentally that T*, Ts and TF depend linearly on the Ca-doping lev el, while the quantity (2 Delta (2)(PS))/(2 Delta (T)) - Delta (T) has a qu adratic-polynomial dependence on the Ca-doping level.