  While the search of high Tc superconductivity was driven mostly by trial and
error methodology searching for novel materials, here we provide a
quasi-first-principle quantum theory for engineering superconductivity in
artificial high-Tc superlattices (AHTS) with period d, ranging from 5.28 down
to 3 nanometers, made of superconducting quantum wells of variable thickness L.
An important feature of our quantum design is the key role of the interface
internal electric field giving Rashba spin-orbit coupling (SOC) in the
nanoscale quantum superconducting building blocks. By tuning the geometrical
conformational parameter L/d around its magic ratio 2/3 we predict the
superconducting dome of Tc versus doping characteristic of unconventional
superconductors. Quantum size effects, controlled by L/d, change the energy
width and splitting of two quantum subbands formed by the electronic space
charge confined in superconducting nano-layers. The theoretical superconducting
dome Tc versus charge density controlled by the Fano-Feshbach resonance between
two superconducting gaps has been able to predict experimental results on
cuprate AHTS by tuning the geometry of superlattices of quantum wells made of
superconducting layers (S) of thickness L of modulation doped stoichiometric
Mott insulator La2CuO4 with no chemical dopants, with interface space charge
confined within normal metal (N) overdoped cuprate layers
