  Recently, the quest for high-Tc superconductivity has evolved from the
trial-and-error methodology to the growth of nanostructured artificial high-Tc
superlattices (AHTS) with tailor-made superconducting functional properties by
quantum design. Superlattices are composed of nanoscale superconducting units
of modulation doped Mott insulator La2CuO4 with thickness L intercalated by
metallic overdoped La1.55Sr0.45CuO4 and period d. Quantum design based on the
multi-gap Bogoliubov theory including spin-orbit coupling (SOC). has been
employed for prediction of the amplification of the critical temperature as a
function of the conformational parameter L/d. At the top of the superconducting
dome, at the magic ratio L/d=2/3, the heterostructures are tuned at the
Fano-Feshbach resonance and the normal phase exhibits the Planckian T-linear
resistivity. Here, we report experimental evidence that the Kondo proximity
effect competes with the Fano-Feshbach resonance suppressing Tc on both sides
of the superconducting dome. The Kondo proximity effect is expected in
electrical resistance of AHTS nanoscale heterostructures following a Kondo
universal scaling obtained by numerical renormalization group theory. We show
the vanishing Kondo temperature TK and Kondo scattering amplitude R0K at
L/d=2/3, while TK and R0K increase on the underdoped (L/d>2/3) and overdoped
(L/d<2/3) side of the superconducting dome.
