By calculation and analysis of the bare conduction bands in a large number
of hole-doped high-temperature superconductors, we have identified the rang
e of the intralayer hopping as the essential, material-dependent parameter.
It is controlled by the energy of the axial orbital, a hybrid between Cu 4
s, apical-oxygen 2p(z), and farther orbitals. Materials with higher T-c (ma
x) have larger hopping ranges and axial orbitals more localized in the CuO2
layers.