We argue that in cuprate physics there are two types , hole content per CuO _ { 2 } plane ( P _ { pl } ) and the corresponding hole content per unit volume ( P _ { 3 D } ) , of hole-doping concentrations for addressing physical properties that are two-dimensional ( 2D ) and three-dimensional ( 3D ) in nature , respectively .
We find that superconducting transition temperature ( T _ { c } ) varies systematically with P _ { 3 D } as a superconducting “ dome ” with a universal optimal hole-doping concentration P _ { 3 D } ^ { opt . } = 1.6 \times 10 ^ { 21 } cm ^ { -3 } for single-layer high temperature superconductors .
We suggest that P _ { 3 D } ^ { opt . } determines the upper bound of the electronic energy of underdoped single-layer high- T _ { c } cuprates .