Electronic and superconducting properties of a superlattice of quantum stripes at the atomic limit

The superconducting gap, the critical temperature and the isotope coefficient in a superlattice of metallic quantum stripes is calculated as a function of the electron number density. We show that it is possible to design a particular artificial superlattice of quantum stripes that exhibits the curves of T _c and of the isotope coefficient as a function of the charge density as in cuprate superconductors. The shape of the superlattice is designed in order to tune the chemical potential near the bottom of the third subband for an electron number density of ρ ～ 5:810-²Å^-2. The superconducting critical temperature shows a resonant amplification as a function of electron number density ρ with a maximum at a critical value ρ _c. The isotope coefficient shows a sharp drop from a regime where α > 0:5 at ρ < ρ _c to a regime where α < 0:2 at ρ ≥ ρ _c. The underdoped and overdoped regime in cuprate superconductors is associated with a transition from a quasi 1D behavior for ρ > ρ _c to quasi 2D behavior for ρ < ρ _c with opening of a pseudogap at ρ ～ ρ _c.