  Emergence, development and cessation of superconductivity in three
representative compounds of copper oxide families---cation doped
Ca_2-xNa_xCuO2Cl2 and La_2-xAe_xCuO4 (Ae = Ba, Sr), as well as oxygen enriched
YBa2Cu3O_6+x ---are explained with the Coulomb-oscillator model of
superconductivity. By the model, non-resistive current is carried by axial
Coulomb oscillations of s electrons through neighbor nuclei---here excited 3s
electrons from O^2- ions through next-nearest neighbor oxygen nuclei---if their
accompanying lateral oscillation is sufficiently confined to prevent lateral
overswing. Cation doping gives rise to a superlattice in the layers that
sandwich each CuO2 plane. In Ca_2-xNa_xCuO2Cl2, having one CuO2 plane per unit
cell, superconductivity emerges when laterally confined Coulomb oscillators
start connecting along 6 x 6 superlattice domains (in units of planar lattice
constants) and it peaks at 4 x 4 domains when, at doping x = 1/8, the
superlattice is completed. With further doping a new, off-set superlattice
grows. Its frustrating effect gradually reduces superconductivity to cessation.
The same mechanism holds for La_2-xAe_xCuO4 which has two, staggered CuO2
planes per unit cell. The staggering causes superconducting frustration or
boost between adjacent layer sandwiches. This results in a double hump of the
transition temperature Tc(x), instead of a dome, with a deep furrow or dip at x
= 1/8 for Ae = Ba or Sr, respectively. Oxygen enrichment of YBa2Cu3O_6+x
indirectly leads to effective doping in the CuO2 planes themselves (Cu^2+ -->
Cu^3+). The ionization of copper ions at the corners of planar unit cells
determines whether lateral oscillations between next-nearest neighbor O^2- ions
overswing (Tc = 0) or are confined to wide or narrow electron tracks. Their
percolating connectivity gives rise to respective plateaus of Tc = 57 K and Tc
= 90 K, and intermediate ramps.
