We propose that physical properties for the high temperature superconductors can be addressed by either a two-dimensional planar hole-doping concentration ($P_{ pl}$) or an effective three-dimentional hole-doping concentration ($P_{ 3D}$). We find that superconducting transition temperature ($T_c$) exhibits a universal dome-shaped behavior in the $T_c$ $vs.$ $P_{ 3D}$ plot with a universal optimal doping concentration at $P_{ 3D}$ $\sim$ 1.6 $\times$ 10$^{ 21}$ cm$^{ -3}$ for the single-layer high temperature superconductors.
Categories: cond-mat.supr-con astro-ph cond-mat.mtrl-sci cond-mat.str-el